. "Fracture mechanics"@en . . "3" . "Not provided" . . "Presential"@en . "FALSE" . . "Introduction to general relativity"@en . . "3" . "The student becomes acquainted with Einstein's theory of relativity and thus with the notion of gravity as a manifestation of curved spacetime.\nThe student learns how to apply the theory in a number of physical situations, correcting his/her intuition where necessary, and he/she studies the experimental foundations and tests of the theory.\nThe student learns to interpret statements about relativity made in the popular scientific literature or in the media in general. He/she learns to appreciate the developments in relativity within the general historical context of physics." . . "Presential"@en . "TRUE" . . "Relativity"@en . . "6" . "The students are introduced to Einstein's theory of gravity. After a short introduction to the basics of differential geometry the Einstein equations are derived and studied. Exact solutions of the Einstein equations and their physical applications are discussed in detail. Various other topics such as black holes, gravitational waves and applications of general relativity to cosmology are also an integral part of this course." . . "Presential"@en . "TRUE" . . "Celestial mechanics (1)"@en . . "7" . "Two-body problem. Central orbits. General integrals of motion. Conservation laws. Relationship between integral constants and orbital parameters. Kepler’s laws. Gauss’s constant, astronomical unit, masses of planets. Energy integral and limits of velocities. Elliptical, parabolic and hyperbolic motion. Solution of Kepler’s equation. Orbit in space. Types of orbits in the Solar system. Ephemeris calculation. Time series. Fundamentals of orbit determination. N-body problem. General integrals. Relative coordinates, concept of preturbations, disturbing function. Introduction to perturbations. Virial Theorem.\n\nOutcome:\nThe course provides an introduction to astrodynamics, two-body problem, basics of orbit determination. Introduction to the n-body problem." . . "Presential"@en . "TRUE" . . "Celestial mechanics (2)"@en . . "4" . "General integrals of the n-body motion. Disturbing function. Perturbed orbits. Small impulses and the change of orbital elements. Lagrange's planetary equations, 1-st order solution. Introduction to resonances. Restricted three-body problem. Jacobi integral. Lagrangian equilibrium points, stable and unstable solution. Tisserand invariant. Gravitational spheres.\r\n\r\nNumerical solution of n-body problem, Cowell and Encke type.\r\n\r\nGravitational potential of a finite body. Perturbations in satellite motion.\n\nOutcome:\nFundamentals of the three-body and the n-body problem. General and special perturbations, secular motion. Motion in the field of a finite body." . . "Presential"@en . "TRUE" . . "General relativity"@en . . "7" . "Description of gravity in general relativity (metric space-time tensor, equations of motion of matter in the gravitational field, Einstein's equations), applications of general relativity (post-Newtonian approximation, relativistic stars and black holes, gravitational waves, relativistic cosmological models)\n\nOutcome:\nAfter completing the course, students will know how the general theory of relativity is constructed and will be acquainted with its most important applications" . . "Presential"@en . "FALSE" . . "Celestial mechanics - state exams"@en . . "2" . "Two-body problem. Central orbits. General integrals of motion. Conservation laws. Relationship\r\n\r\nbetween integral constants and orbital parameters. Kepler’s laws. Gauss’s constant, astronomical\r\n\r\nunit, masses of planets. Energy integral and limits of velocities. Elliptical, parabolic and hyperbolic motion. Solution of Kepler’s equation. Orbit in space. Types of orbits in the Solar system. Ephemeris calculation. Time series. Fundamentals of orbit determination.\r\n\r\nN-body problem. General integrals. Relative coordinates, concept of preturbations, disturbing function. Virial Theorem. General integrals of the n-body motion. Disturbing function. Perturbed orbits. Small impulses and the change of orbital elements. Lagrange's planetary equations, 1-st order solution. Introduction to resonances.\r\n\r\nRestricted three-body problem. Jacobi integral. Lagrangian equilibrium points, stable and unstable solution. Tisserand invariant. Gravitational spheres.\r\n\r\nNumerical solution of n-body problem, Cowell and Encke type.\r\n\r\nGravitational potential of a finite body. Perturbations in satellite motion.\n\nOutcome:\nThe students will proof the understanding of two and n body problem." . . "Presential"@en . "TRUE" . . "Mechanics and strength of composite materials"@en . . "6" . "The study course will be dedicated to the structures of layered fibre materials, their features and requirements in aviation structures. The use of composite materials in the construction of aviation structures, application, definitions, classification, characteristics, mechanics and strength are considered.\n\nOutcome:\nAble to use stress and strain processes in the loading of composite materials. - Practical work. Examination.\r\nAble to use analysis component in the construction of composite materials. - Practical work. Examination.\r\nAble to calculate the strength of composite materials. - Practical work. Examination.\r\nAble to create composite materials with preconditioned qualities. - Practical work. Examination.\r\nAble to create optimal construction projects with composite materials. - Practical work. Examination." . . "Presential"@en . "TRUE" . . "High-energy astrophysics and gravitational wave astrophysics"@en . . "6" . "To give an overview of the high-energy phenomena that are observed in the Universe\nTo connect these observations to the relevant physics\nTo obtain a deeper understanding of physics under extreme temperatures, densities, pressures and gravitational fields" . . "Presential"@en . "TRUE" . . "Relativity"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "Applied numerical fluid mechanics"@en . . "3" . "Introduction of CFD (I), Introduction of CFD (II), Turbulence modeling (I), Multiphase \r\nflow II, Computational heat transfer, Convection in porous media (I), Convection in \r\nporous media (II), Multiphase flow (I), Computational combustion (I), Computational \r\ncombustion (II), Introduction of OpenFoam, Summary\n\nOutcome: Not Provided" . . "Presential"@en . "FALSE" . . "High-energy astrophysics and gravitational wave astrophysics"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "Engineering mechanics"@en . . "9" . "no data" . . "Presential"@en . "TRUE" . . "Mechanics and thermokinetics of space systems"@en . . "5" . "Learning outcomes of the course unit:\nStudent is able to analyze satellite components as well as whole satellite from viewpoint of structural stiffness and heat transfer. Student is able to analyze structural satellite design loaded by static and dynamic forces. He is able to perform a modal, harmonic and transient analysis of satellite components using Finite Element Method (FEM). Student is able to realize heat transfer analyzes of individual components considering individual heat transfer modes. Student is able to perform, similarly to structural analysis, thermal analysis using FEM. Course Contents:\nSatellite structures and materials. Satellite subsystems. Satellite structural design. Strength analysis of space systems. Static strength analysis. Modal analysis. Harmonic response analysis. Thermal deformation analysis.Spacecraft structural analysis using finite element method.Heat transfer mechanisms. Conductive heat transfer. Fourier's law of heat conduction. Convective heat transfer. Newton's law of cooling. Radiative heat transfer. Stefan-Boltzmann law. Heat generated by the spacecraft electronics. Passive and active thermal control. Spacecraft thermal analysis using finite element method." . . "Presential"@en . "FALSE" . . "Quantum mechanics IIa"@en . . "5" . "LEARNING OUTCOMES\nThe student knows the formalism on non-relativistic quantum mechanics. The student can apply perturbation theory and other approximation methods to time-dependent perturbations and scattering problems in atomic, nuclear and condensed matter physics. The student understands the assumptions underlying different approximations and can estimate the range of validity of different approximation methods within the considered context. The student can couple three angular momenta, knows spherical tensor operators and can apply Wigner-Eckart theorem.\n\nCONTENT\nTime dependent perturbation theory, Fermi's Golden rule, sudden and adiabatic approximations.\nScattering theory: construction of Lippmann-Schwinger equation and its solution in Born approximation.\nScattering theory: partial wave method for spherically symmetric potentials, scattering resonances.\nCoupling of angular momenta, spherical tensor operators and Wingner-Eckart theorem.\nPath integral formulation of quantum mechanics" . . "Presential"@en . "FALSE" . . "Quantum mechanics IIb"@en . . "5" . "LEARNING OUTCOMES\nThe student knows the methods of second quantisation in non-relativistic many-body quantum mechanics and can apply these. The student can quantize free boson and fermion fields. The student can quantize electromagnetic field and apply the theory to describe interaction of quantised matter and radiation.\n\nCONTENT\nMany-particle methods in non-relativistic quantum mechanics\nElements of quantum field theory.\nQuantum theory of radiation." . . "Presential"@en . "FALSE" . . "Flight and orbital mechanics and propulsion"@en . . "6" . "no data" . . "Presential"@en . "TRUE" . . "General relativity I"@en . . "5" . "LEARNING OUTCOMES\nYou will learn the physical and mathematical structure of the theory of general relativity.\n\nYou will learn how to do calculations in general relativity, including how to find the precession of the orbit of Mercury and the bending of light by the Sun.\n\nCONTENT\nChapter 1: review of symmetries in Newtonian mechanics, review of special relativity from the spacetime point of view, relativity principle in Newtonian mechanics and special relativity, electrodynamics in special relativity\n\nChapter 2: the equivalence principle, manifolds, tensors, the metric\n\nChapter 3: covariant derivative and connection, parallel transport, geodesics, curvature, Riemann tensor\n\nChapter 4: Einstein equation, Newtonian limit\n\nChapter 5: The Schwarzschild solution, precession of the perihelion of Mercury, bending of light by the Sun" . . "Presential"@en . "FALSE" . . "General relativity II"@en . . "5" . "LEARNING OUTCOMES\nYou will learn the physical and mathematical structure of the theory of general relativity.\n\nYou will learn how to do calculations in general relativity, including with black holes, linear perturbation theory, gravitational waves and a little bit also in cosmology.\n\nCONTENT\nChapter 1: action formulation of general relativity\n\nChapter 2: global structure of the Schwarzschild solution, black holes, Penrose diagram, brief overview of charged and rotating black holes and Hawking radiation\n\nChapter 3: perturbation theory around Minkowski space, gauge transformations, gravitomagnetism, gravitational waves, generation of gravitational waves by a binary system, energy loss due to emission of gravitational waves\n\nChapter 4: Killing vectors, symmetric spacetimes, FLRW spacetime, de Sitter space, anti-de Sitter space, Penrose diagrams" . . "Presential"@en . "FALSE" . . "Gravitational lensing"@en . . "5" . "LEARNING OUTCOMES\nThe course gives you the theoretical basis to understand gravitational lensing as a physical phenomenon. You will understand the relation between lensing theory and observations, and how lensing can be used to extract cosmological information. You will have the conceptual basis that allows you to deepen your knowledge by reading further literature or publications.\n\nCONTENT\nGravitational lensing is a powerful cosmological probe. This course is an introduction to the theory of gravitational lensing in the context of cosmology. The theory is built on the theory of general relativity, and on the FRW model of the universe. The focus is on cosmology, thus we will mainly be working at the weak-lensing limit, strong lensing is touched only briefly.\n\nThe course is motivated by Euclid, the European Space Agency’s satellite mission to probe the large scale structure and expansion history of the universe. The course forms a natural continuation to the course of Galaxy Survey Cosmology, but can also be taken individually.\n\nContents:\n\n- Propagation of light in general relativity\n\n- Lensing geometry and basic concepts\n\n- Weak and strong lensing\n\n- Magnification and distortion\n\n- Relation to observations\n\n- Lensing as a cosmological probe\n\n- Shear field, E- and B-modes\n\n- Lensing spectrum and correlation function\n\n- Shear as a spin-2 field" . . "Presential"@en . "FALSE" . . "Space flight mechanics"@en . . "3" . "LEARNING OUTCOMES OF THE COURSE UNIT\n\nLearning basic principles of space flight mechanics. Acquiring knowledge of aerospace techniques (launchers, space vehicles and stations).\n\nAIMS\n\nThe goal is to familiarize students with the branch of the area of aeronautical and cosmic means of transport that develops in a progressive way and with main problems of space flights.\nSYLLABUS\n1. Historical introduction to astronautics.\n2. Basic problems of space flight and its technical solutions.\n3. Definition and clasification of space vehicles. Coordinate systems in mechanics of space flight.\n4. Passive motion in a central gravitational field. Kepler's laws.\n5. Position and velocity of cosmic bodies in orbit. Integral energy.\n6. Description orbit. Orbit elements.\n7. Active motion of space vehicles. Dynamics of rocket motion.\n8. Flight performance of space vehicles. Specific impulse.\n9. Launch of artificial Earth satellite. Characteristic of space velocities.\n10. Maneuvering in orbit. Active-controlled movement of space vehicles.\n11. Meeting spacecraft in orbit.\n12. Interplanetary space flight.\n13. Re-entry problems.\n\nEXERCISE\n\n13 hours, compulsory\nTEACHER / LECTURER\n\nIng. Jaroslav Bartoněk\nSYLLABUS\n\n1. Calculations of basic parameters of the orbit in the central gravitational field.\n2. Time course of motion of a cosmic body - solution of Kepler's equation.\n3. Calculation of position and velocity of a body in the perifocal coordinate system.\n4. Calculation of position and speed using Lagrange coefficients.\n5. Position and velocity of a cosmic body in orbit in space.\n6. Transformation between geocentric and perifocal coordinate system.\n7. Determination of orbit elements from the state vector.\n8. Calculation of the position of a body in topocentric horizontal coordinates. system.\n9. Flight performance of single-stage and multi-stage missiles during vertical takeoff.\n10. Coplanar changes in orbit and change in inclination of the orbit.\n11. Calculation of the general transition path between two circular paths.\n12. Hohmann transition path.\n13. Bieliptic transition path." . . "Presential"@en . "TRUE" . . "Applied mechanics"@en . . "6" . "Description is not available" . . "Presential"@en . "TRUE" . . "Rational mechanics"@en . . "6" . "The aim of the course is to present the main topics of classical mechanics, in the Newtonian and Lagrangian formulation." . . "Presential"@en . "TRUE" . . "Structural mechanics"@en . . "12" . "Learning outcomes\n\nThe course’s main objective is to give to students the ability to analyze the mechanical behaviour of structures that can be modelled as systems of elastic beams. To this end, it aims to furnish a coherent rational introduction to the mechanics of structures.\nAs a second objective, students are taught the fundamental notions of the classical theory of linear elasticity and consequently develop the ability to analyze the mechanical behaviour of solid bodies modelled as elastically deformable continuous bodies. Lastly, students will develop an understanding of the two failure modes for the elastic behaviour of structures: the first due to the outcoming of inelastic deformations, with increasing external loads; the second resulting from rising instability phenomena affecting the equilibrium." . . "Presential"@en . "TRUE" . . "Fluid dynamics"@en . . "12" . "Learning outcomes\n\nThe objective of the course is to introduce the equations and the fundamental physical features of fluid dynamics, and to explain the mechanisms that are at the basis of the generation of the aerodynamic loads on moving bodies. At the end of the course the students should be able of using the methodologies for the prediction of the aerodynamic loads acting on bodies of different geometry, and in particular on aircrafts in subsonic motion." . . "Presential"@en . "TRUE" . . "advanced statistical mechanics - kul - see hyperlink below*"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "classical and celestial mechanics"@en . . "5" . "The topics covered by the course include: 1) The fundamental concepts of Newtonian mechanics and the gravitational potential theory, gravitational potential outside uniform spheroid and due to uniform disk (ring), motion in rotating reference frames, elements of the rigid body dynamics, basic concepts in the Lagrangian mechanics. 2) The N-body problem in the classical framework, the first integrals of the equations of motion, the virial theorem, the dark matter concept, planetary N-body problemn and the equations of motion in relative coordinates, Jacobi and Poincare variables. 3) The Taylor integration scheme for the ordinary differential equations (ODE) as the canonical method of solving the equations of motion in classical and celestial mechanics, perturbed two body problem (e.g., due to relativistic and non-point mass interactions). 4) The theory of motion in central force fields, qualitative analysis of systems with one-degree of freedom, the two body problem, elements of conic curves theory, Keplerian laws, classification and parametrisation of Keplerian orbits (geometric and dynamical elements), simple models of motion in galactic gravitational environments (such as the Henon-Heiles model, the logarithmic, and the Yukawa potentials). 5) Orbits of the planets in the Solar System, the figure of the Earth, tidal interactions among the Earth, Moon, and Sun, the secular evolution and the long-term stability of the Solar system. 6) The two-body orbits kinematic fitting (the Neutsch method) and the merit function for observations made with various techniques (astrometry, eclipse timing, radial velocities), determining the mass function and orbits of binary stars and extrasolar planetary systems. 7) The circular and elliptic restricted three body problems as the fundamental models for astrodynamics (motion of man-made objects in space) and a non-trivial generalisation of the Kepler problem, libration points, elements of the stability and deterministic chaos theory." . . "Presential"@en . "TRUE" . . "general relativity"@en . . "6" . "List of topics: 1. Recollection of tensor analysis 2. Symmetric spaces 3. Conservation principles 4. Relativity principles 5. Einstein’s general relativity equations 6. Schwarzschild’s solution of Einstein’s equations for spherically symmetric case in vacuum 7. Observable effects of general relativity theory 8. Friedmann’s solutions – cosmological models 9. Gravitational waves" . . "Presential"@en . "TRUE" . . "Quanta, particles and relativity"@en . . "no data" . "no data" . . "Presential"@en . "TRUE" . . "Applied mathematics: mechanics and methods"@en . . "no data" . "no data" . . "Presential"@en . "TRUE" . . "Introductory quantum mechanics"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Classical mechanics & relativity"@en . . "no data" . "Students will acquire an understanding of the foundations of classical mechanics and special relativity as well as their applications and uses in other areas of physics. Students will be able to analyse, understand and describe model systems and physical experiments, and be able to apply this knowledge to solve quantitative problems." . . "Presential"@en . "FALSE" . . "Quantum mechanics"@en . . "no data" . "The emphasis of this course is on analyzing the basic concepts underpinning Quantum Theory and building up the necessary skill set to tackle problems in Quantum Mechanics. On completion, students should have a good understanding of quantum phenomena and be able to be able to apply fundamental quantum mechanics to a range of problems on idealized systems." . . "Presential"@en . "FALSE" . . "General relativity & cosmology"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Applied quantum mechanics"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "quantum mechanics 2"@en . . "10" . "no data" . . "Presential"@en . "FALSE" . . "Continuum mechanics"@en . . "10" . "no data" . . "Presential"@en . "FALSE" . . "Engineering mechanics"@en . . "6" . "Statics includes the concepts and principles of statics, reduction of\nforce systems and equilibrium conditions, laws of friction and the\ncalculation of centres of gravity. Strength of materials includes the\nbasic concepts of strength of materials, tension, compression,\nbending, torsion and buckling, characterisation of multidimensional\nstress states, deflection calculations of beams and plane trusses.\nKinematics includes the basic concepts and terms of kinematics,\npoint kinematics, rigid body motion, compound point motion, plane\nmotion, and spherical rigid body motion. Dynamics includes the\nbasic concepts and definitions of dynamics, dynamics of a point and\nsystem of material points, dynamics of rotary motion and motion of" . . "Presential"@en . "TRUE" . . "Fluid mechanics"@en . . "4" . "Description of fluid state and motion, kinematics elements, velocity\ncirculation. Local motion of a fluid element, deformation velocity ten-\nsor and stress tensor. Basic equations of fluid mechanics,\nNavier-Stokes equation, similarity of flows. Elements of hydrostat-\nics - equilibrium equation, hydrostatic thrust and buoyancy, stand-\nard atmosphere. Euler's equation of motion, Bernoulli's equation,\nelements of applied hydraulics. Laminar and turbulent motion,\nboundary layer, Prandtl equation, Karman equation.\nKarman equation. “Well and badly” flowing bodies, issues of bound-\nary layer detachment, effect of detachment on aerodynamic coeffi-\ncients. Wave phenomena, effect of gas compressibility, isentropic\nflows." . . "Presential"@en . "FALSE" . . "Fluid mechanics and aerodynamics"@en . . "4" . "Description of fluid state and motion, local motion of a fluid element,\ndeformation velocity tensor and stress tensor. Basic equations of\nfluid mechanics, similarity of flows. Equation of equilibrium of a fluid,\nstandard atmosphere. Euler's equation of motion, Bernoulli's equa-\ntion, boundary layer issues, boundary layer detachment. Determi-\nnation of basic flow parameters. Wave phenomena, effects of gas\ncompressibility.\nIntroduction to aerodynamics, aerodynamic objectives and re-\nsearch methods in aerodynamics. Airfoil theory: description of ge-\nometry, aerodynamic characteristics of the airfoil. Lifting surface:\ndescription of geometry, aerodynamic characteristics. Subcritical\nand supercritical airfoil and wing flow. Elements of high speed aer-\nodynamics." . . "Presential"@en . "FALSE" . . "Basics of flight mechanics"@en . . "3" . "Flight mechanics objectves, forces acting on the aircraft. Dynamics\nof aircraft motion as a material point. Motion of aircraft on rectilinear\ntrajectories inclined at any angle. Aircraft transient motions on rec-\ntilinear and curvilinear tracks in the vertical and horizontal plane and\non space tracks. Issues of aircraft take-off and landing, aerody-\nnamic characteristics in take-off and landing configurations. Dy-\nnamics of aircraft motion as a material solid. Aircraft equilibrium,\nstatic stability and longitudinal controllability. Equilibrium, static sta-\nbility and lateral controllability, aircraft equilibrium curve. Moments" . . "Presential"@en . "FALSE" . . "Flight mechanics"@en . . "6" . "Flight mechanics tasks, forces operating on the aircraft (SP). Dy-\nnamics of aircraft motion as a material point. Aircraft motions on\nrectilinear trajectories inclined at any angle. Aircraft transient motion\non vertical and horizontal straight and curvilinear tracks and on\nspace tracks. SP take-off and landing issues, aerodynamic charac-\nteristics in the take-off configuration and in the landing configura-\ntion. Dynamics of SP motion as a material solid. Equilibrium, static\nstability and longitudinal controllability of aircraft. Equilibrium, static\nstability and lateral controllability, aircraft equilibrium curve. Mo-\nments acting on an aircraft in transient motion. Peculiarities of air-\ncraft flight at large angles of attack. Suborbital and orbital flights of\nspacecraft." . . "Presential"@en . "FALSE" . . "Flight mechanics"@en . . "6" . "Flight mechanics objectives, forces acting on the aircraft (SP). Dy-\nnamics of aircraft motion as a material point. Aircraft motions on\nrectilinear trajectories inclined at any angle. Aircraft transient motion\non vertical and horizontal straight and curvilinear tracks and on\nspace tracks. SP take-off and landing issues, aerodynamic charac-\nteristics in the take-off configuration and in the landing configura-\ntion. Dynamics of SP motion as a material solid. Aircraft equilibrium,\nstatic stability and longitudinal controllability. Equilibrium, static sta-\nbility and lateral controllability, aircraft equilibrium curve. Moments\nacting on an aircraft in transient motion. Peculiarities of aircraft flight\nat large angles of attack. Suborbital and orbital flights of spacecraft." . . "Presential"@en . "FALSE" . . "General relativity and gravitation"@en . . "6" . "Special Theory of Relativity: Minkowski spacetime, Lorentz transformations, accelerated\nobservers. Einstein’s Equivalence Principle. Tensor calculus. Manifolds and tensor fields.\nAffine and metric geometry: conncection, parallel transport, metric, geodesics, curvature.\nEnergy-momentum tensor. Einstein's equations. Newtonian limit. Tests of General Relativity.\nSchwarzschild's geometry, black holes, hydrostatic equilibrium of stars. Cosmology:\nFriedmann's equations. accelerated expansion, dark energy, dark matter. Gravitational\nwaves." . . "Presential"@en . "TRUE" . . "Advanced general relativity"@en . . "6" . "From Newton to Einstein: conceptual foundations of general relativity. Motion of particles and\ngeodesic equation. Geodesic deviation and curvature. Energy momentum tensor and Einstein\nequations. Gravitational waves, theory and observations. Black holes, theory and\nobservations. Gravitational lensing, theory and observations. Some modern developments in\ngeneral relativity." . . "Presential"@en . "FALSE" . . "Gravitational waves"@en . . "3" . "Einstein's equations, linear approximation, post-Newtonian approximation. Mathematics and\nphysics of gravitational waves. Astrophysical and cosmological sources of gravitational\nradiation. Gravitational waveforms of binary systems. Detection of gravitational waves." . . "Presential"@en . "FALSE" . . "Relativity"@en . . "2" . "The principle of special relativity. Minkowski spaceime. Relaivisic kinemaics, velocity addiions, Lorentz transformaion, ime dilataion, Lorentz contracion. Astrophysical applications: superluminal moions, relaivisic beaming. Relaivisic dynamics. 4-vectors, mass increase. Principle of general relativity. Curved manifolds, curved spaceime, covariant and contravariant representaion. Einstein equaions. Robertson-Walker metrics, Schwarzschild and Kerr metrics. Astrophysical applicaions: perihelion moion, light delecion, dynamics around black holes." . . "Presential"@en . "TRUE" . . "Celesial mechanics 1-4"@en . . "8" . "Semester 1: General perturbaion theory\nCanonical perturbaion theory: Hamilton-Jacobi method, acion-angle variables. The fundamental theorem of perturbaion theory, Delaunay's lunar theory and eliminaion method. Poincaré-Zeipel method. Theory of resonant perturbaions. Lie transform perturbaion theory. Superconvergent perturbaion theory. Ordered and chaoic moions: KAM theory.\nOrdered and chaoic orbits in the restricted three-body problem. Lyapunov indicators. Poincaré mappings. Hénon-Heiles problem. Symplecic mappings, symplecic integrators.\nSemester 2: Dynamics of planetary systems\nResonances of irst and second order. Resonant encounters, capture into and passing through a resonance. Muliple resonances.Resonances in the Solar System.\nDynamics of the Solar System: Moion of giant planets. Stability of the Solar System. Rotaion of the planets and moons. Dynamics of resonant asteroids.\nExoplanetary systems: Dynamical classiicaion of muliple planetary systems. Resonant, interacing and hierarchical systems. Planet-disk interacions. Stability of exoplanetary systems.\nSemester 3: The three-body problem\nThe general three-body problem: Equaions of moion and irst integrals. The Lagrange-Jacobi equaion. Classiicaion of inal coniguraions. The Euler-Lagrange soluions.\nThe restricted three-body problem: Equaions of moion, the Jacobi-integral. Equilibrium soluions and their stability. Zero velocity curves. Regularizaion transformaions. Periodic and numerical soluions. The ellipic restricted three-body problem. The Hill-problem.\nSemester 4: Theory of ariicial satellites\nThe gravitaional potenial. Terrestrial gravitaional perturbaions.\nLunisolar perturbaions. Non-gravitaional perturbaions." . . "Presential"@en . "TRUE" . . "Computational fluid dynamics"@en . . "6" . "no data" . . "Presential"@en . "FALSE" . . "Structural mechanics of aircraft structures"@en . . "4" . "Thinwalled beams; Variational methods; Plates and shells; Displacements in aircraft structures; Plastic deformations; Composite materials" . . "Presential"@en . "FALSE" . . "Fracture mechanics"@en . . "3" . "no data" . . "Presential"@en . "FALSE" . . "Engineering mechanics - statics"@en . . "no data" . "This module provides a grounding in the fundamental principles of engineering mechanics. Students will gain knowledge and understanding of the common and important material properties for various engineering applications." . . "Presential"@en . "TRUE" . . "Engineering mechanics and materials II"@en . . "no data" . "This module provides a grounding in the fundamental principles of engineering mechanics. Students will gain knowledge and understanding of the common and important material properties for various engineering applications and problem solving." . . "Presential"@en . "TRUE" . . "Solid mechanics and intro to fea"@en . . "no data" . "This module helps to establish a solid foundation for the analysis of solids and structures based on the fundamental principles of continuum mechanics. Students learn to link models and engineering applications with a range of real-life examples, experimental testing and comparative analysis of experimental measurements and theoretical results." . . "Presential"@en . "TRUE" . . "Flight mechanics and aircraft design"@en . . "no data" . "This module introduces the basic principles of aircraft flight performance, stability and control, and aircraft design." . . "Presential"@en . "TRUE" . . "Mechanics"@en . . "3" . "no data" . . "Presential"@en . "TRUE" . . "Space mechanics and airworthiness"@en . . "no data" . "This module introduces students to aspects of the mechanics of space and orbit flight and fundamental concepts of atmospheric re-entry and atmospheric heating. Students will learn introduction to aircraft airworthiness requirements and regulations and explain how to meet these requirements in aircraft design and manufacture." . . "Presential"@en . "TRUE" . . "Mechanics 2"@en . . "5" . "no data" . . "Presential"@en . "TRUE" . . "Mechanics of structures 1"@en . . "4" . "To learn fundamentals of deformable bodies mechanics: stress, strain, material behavior as a introduction to structural analysis and design for static loads. Presenting concepts of statical structural analysis: equilibrium conditions, stress-strain relation (Hooke’s law) and structure deformation. Develop knowledge for strength analysis of one-dimensional structures in basic load cases: tension-compression, torsion and bending." . . "Presential"@en . "TRUE" . . "Continuum mechanics"@en . . "6" . "• Basic concepts regarding Cartesian tensors, Lagrangian and Eulererian coordinates\n• Strain tensor, deformation, conservation laws, constitutive equations\n• Linear elasticity, Navier equations\n• Newtonian fluid mechanics, Navier-Stokes equations, ideal fluids, vorticity\n• Viscous fluids, laminar flow, turbulent flow, boundary layer, aerodynamics\n• Thermodynamics of continua\n• Applications of the Euler equations: solar wind, stellar stability, Newtonian cosmology\n• Waves and solitons (Korteweg-de Vries)\n• Electromagnetic continuum in plasmas, magnetohydrodynamics (MHD), plasma waves\n• Concepts from modern differential geometry: vector fields and differential forms, tensor\n• analysis, Riemannian geometry\n• Nonlinear continua\n• Structural elements: beams, plates and shells\n• Geometry and gauge theory in fluid mechanics\n• Relativistic continuum, energy-momentum tensor, Einstein field equations, cosmology.\nFinal competences:\n1 The student has gained insight in the foundations of the mechanics of continuous media.\r\n2 The student has gained appreciation for the interdisciplinary character of the domain of\r\ncontinuum mechanics and of the common applicability of the underlying physical principles\r\nand the mathematical formalism in the multiple specialties wherein applications were\r\nprovided.\r\n3 The student is able to use the acquired expertise to translate physical problems into\r\nmathematical models and, conversely, to interpret mathematical conclusions in a physical context.\r\n4 The student has acquired arithmetic skills, both analytical and by computer, allowing him/herto solve new problems in continuum mechanics, starting from the insight gained.\r\n5 The student has acquired the necessary skills to commence a more specialized study in each of the subdisciplines discussed." . . "Presential"@en . "FALSE" . . "General relativity"@en . . "6" . "The first half of the course focuses on the foundations of general relativity, including the underlying mathematical formalism (basic concepts of differential geometry).\n\nThe second half focuses on a selection of important applications (black holes, gravitational waves, cosmology).\nGENERAL COMPETENCIES\r\nCompleting this course should enable students to\r\nexplain main concepts and results in general relativity, Einstein's description of gravity;\r\napply this understanding in practical calculations;\r\nunderstand main aspects of the physics of black holes, gravitational waves;\r\ntake on more advanced topics in general relativity, black hole physics, cosmology." . . "Presential"@en . "TRUE" . . "Fluid mechanics 1"@en . . "4" . "Basic concepts and theoretical constructs of the mechanics of continuum, summary of necessary\n mathematical tools.\n Fluid statics: basic theory and engineering applications.\n Fluid kinematics: description of fluid motion and deformation\n Fluid dynamics: stress in fluids, equations of motion, energy equation, Bernoulli equation, calculation of dynamic reactions, etc.\n Selected models of fluid flow: flow in pipes, boundary layer.\n Elementary introduction to turbulent flows. Good knowledge of the fundamental concepts and principles of the Fluid Mechanics, skills in solving\n basic problems in fluid statics and dynamics of an ideal and viscous liquid." . . "Presential"@en . "TRUE" . . "Aerodynamics and flight mechanics"@en . . "no data" . "Anotation:\r\n\r\nThe course provides overview of key findings from aircraft aerodynamics and flight mechanics. In the first part, students are familiar with models and equations for the flow of an incompressible fluid. In the second part there are derived equations describing force and rotating effects of flow on the surface of the airfoils and wings. The important relations for effects of compressibility are derived in the next part. These findings are applied on flow around the airfoils and wings at high subsonic, supersonic and hypersonic speeds in last part. In the subject there are discussed basic modes of flight mechanics.\r\nCourse outlines:\r\n\r\n1.\t \tProperties of gases, flow models, basic equations of fluid mechanics and thermodynamics.\r\n2.\t \tNavier-Stokes equation. Potential flow, lift. Properties of vortex and vortex fields.\r\n3.\t \tDimensional analysis and similarity, empirical relation for lift. Laminar and turbulent flow. Boundary layer.\r\n4.\t \tAirfoil, aerodynamic force and moment. Theory of thin profile, integral characteristics of the airfoil.\r\n5.\t \tInfluence of boundary layer on the integral characteristics of airfoils. Methods of singularities, panel methods.\r\n6.\t \tGeometry of wing. Theory of wing, induced parameters. Monoplane equation and its solution. Influence of ground plan shape and twist of wing.\r\n7.\t \tDevices for increasing of lift. The concept of the longitudinal and directional stability.\r\n8.\t \tEffects of compressibility. Critical Mach number, transonic divergence, swept wing.\r\n9.\t \tPropulsive system. Theory of propeller propulsion. The main rotor of the helicopter. Turbine jet engine.\r\n10.\t \tFlight mechanics - gliding, horizontal, rising flight, steady horizontal turn, takeoff, landing. Standard atmosphere.\r\n11.\t \tSupersonic flow, critical state. Shock and expansion wave. Supersonic flows around oblique plate.\r\n12.\t \tSupersonic flow around the airfoil and wing. Integral characteristic, wave drag. Transonic flow.\r\n13.\t \tHypersonic flow, flight through the atmosphere. Rocket propulsion, single- and multi-stage rocket. Laval nozzle.\r\n14.\t \tRe-entry capsule, ballistic descent, aerodynamic heating, stability of return module.\r\nExercises outline:\r\n\r\n1.\t \tFlow in duct, calculation of losses. Individual student project.\r\n2.\t \tModelling of the flow, program Matlab/Simulink.\r\n3.\t \tNumeric solution of flow fields, CFD program Fluent.\r\n4.\t \tIntegral characteristics of the profile.\r\n5.\t \tDesign of profile of desired properties.\r\n6.\t \tAirfoil and panel methods.\r\n7.\t \tIntegral characteristics of of the wing.\r\n8.\t \tDesign of wing. Effect of flaps and wing torsion.\r\n9.\t \tWing and panel methods.\r\n10.\t \tDesign of tail surfaces, stability and maneuverability.\r\n11.\t \tDesign of propeller, method of elemental profile.\r\n12.\t \tFlight Mechanics.\r\n13.\t \tIzoentopic flow, critical conditions, Laval nozzle.\r\n14.\t \tBallistic descent." . . "no data"@en . "TRUE" . . "Gravitational lensing"@en . . "6" . "At the end of the course, the student will acquire the basic knowledge of the theory of gravitational lensing, and will be able to discuss the applications of lensing in different astrophysical branches. In particular, the student will be able to distinguish between different regimes of lensing (strong, weak, etc) and will learn through examples how to carry out lensing analyses. The basics of the Python programming language will also be taught to allow the students to better understand the examples and work on small projects." . . "no data"@en . "FALSE" . . "Gravitational wave astrophysics and cosmology"@en . . "6" . "The aim of the course is to provide the student with fundamental knowledge of the physics of gravitational waves and of the importance of gravitational radiation in astrophysics and cosmology. From the theoretical point of view, the student will be able to derive the relevant equations in the framework of general relativity and to describe quantitatively the process of emission of gravitational waves from simple astrophysical sources. From the experimental point of view, the student will understand the basics of gravitational wave detection, with specific applications to current and forthcoming observatories. The student will also get expertise on the methods to extract astrophysical and cosmological information from gravitational wave signals." . . "no data"@en . "FALSE" . . "Astrophysical fluid dynamics"@en . . "6" . "The aim of the course is to provide the student with the main theoretical tools to study the dynamics of fluids in astrophysical systems such as stars, accretion discs, galaxies and clusters of galaxies. At the end of the course the student will be familiar with the analytic modelling of hydrodynamic-equilibrium configurations of fluids in gravitational potentials, of gas flows and of hydrodynamic instabilities. In addition the student will have some knowledge of the role of magnetic fields in the dynamics of astrophysical fluids." . . "no data"@en . "FALSE" . . "Relativity"@en . . "6" . "At the end of the course, the student knows the main elements of special relativity and general relativity, the main experimental tests in their support, and the geometric interpretation in terms of spacetime. In particular, the student becomes familiar with relativistic mechanics as well as the use of Einstein's equations for studying gravitational waves, spherically symmetric solutions, and basic properties of black holes." . . "no data"@en . "FALSE" . . "Mechanics of structures 2"@en . . "2" . "no data" . . "Presential"@en . "TRUE" . . "Introductory mechanics lecture"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Classical mechanics"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Quantum mechanics"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Optimal control and game theory in flight mechanics"@en . . "6" . "The course of Optimal Control and Game Theory in Flight Mechanics aims at providing sophisticate theoretical and \r\nnumerical tools for the design of advanced aerospace missions and operations. Relevant study cases selected from real \r\nmission scenarios will be simulated using GMAT, Matlab/Simulink software. The course is organized as follows: \r\n(1) Theoretical background and introduction to optimal control: The basic concepts of astrodynamics and flight \r\nmechanics are reviewed. Emphasis is given to the mathematical and technical tools which will be used during the \r\nfollowing classes. \r\n(2) Optimal rocket trajectories and control: The problem of optimal control is introduced considering applications on \r\nrocket moving in the atmosphere. The module covers: optimal solutions to the problem of orbit injection (with \r\nimpulsive and continuous thrust, staging and constrained performance of the actuators), optimal pitch control, \r\noptimal staging and sub-optimal guidance suitable for real-time implementation. Several guidance laws are \r\ncompared together with numerical methods to solve the optimization problem. Exact and numerical solutions are \r\ndiscussed, providing the student the knowledge to apply the most appropriate one depending on the operative \r\nscenario under investigation. \r\n(3) Optimal orbital maneuvers: The problem of orbital transfer in the presence of perturbations and in the multi-body \r\nenvironment is studied. The characterization of low-energy trajectories existing in such a dynamical framework is \r\npresented and optimal guidance strategies for low-thrust transit and ballistic captures are developed. At the end of \r\nthis block, the students will manage advanced tools for designing modern low-energy / low-thrust missions. \r\n(4) Dynamic game theory in flight mechanics: Dynamic game theory is introduced to investigate the motion of two \r\nnoncooperative space vehicles. A variety of scenarios, including operations between two spacecraft in proximity \r\n(space) and missile interception (atmosphere), are modeled as zero-sum dynamic games. Numerical solutions for the \r\nmentioned scenario are discussed, introducing the students to the problem of optimization in multi-spacecraft \r\nenvironment. \r\nRelevant study cases selected from real mission scenarios will be simulated using GMAT, Matlab/Simulink software." . . "Presential"@en . "FALSE" . . "Flight mechanics of launch and reentry systems"@en . . "6" . "Launch toward East: advantages. The ECI Frame and orbital parameters (target conditions). The EFI frame and the Launch site equation. Launch windows. Launch sites. Launch systems from movable platform. Tsiolkovsky Formula. \r\nSingle stage to orbit ? Optimal Staging. \r\nPlanar equation of motion and Losses Equation. Gravity losses. Phases of flight. Stage re-entry and dispersion ellipses. \r\nGeneral equation of flight. Ballistic Reentry. Peak of heat and peak of load. Entry corridor evaluation. Entry with lift. \r\nEntry Capsule control. \r\nThe Flat Earth approximation. \r\nThe SCOUT launcher. Engines and actuators. Aerodynamic data. Stage separation. Q-Guidance. \r\nICBM re-entry. \r\nCHASER: AIM-9X Sidewinder Aerodynamic stability derivatives from A11, actuator (canard fin deflection) and sensors \r\n(acceleration and rate gyro) \r\nInterception Algos: Pure Pursuit (PP) guidance. Interception Algos: Collision Triangle and Proportional Navigation \r\n(PN) guidance. Interception Algos: Augmented Proportional Navigation (APN guidance). CHASER: Short period \r\ndynamics @ two different combat scenarios.\r\n(topics in italic are additional ones, mandatory for students following MBDA course)" . . "Presential"@en . "FALSE" . . "Quantum mechanics"@en . . "9" . "not available" . . "Presential"@en . "TRUE" . . "Relativity and cosmology"@en . . "9" . "not available" . . "Presential"@en . "TRUE" . . "Celestial mechanics and dynamical systems"@en . . "6" . "The course aims at providing the students with an introduction to the problem of N self-gravitating bodies. Applications in Celestial Mechanics and Galactic Dynamics are shown." . . "Presential"@en . "FALSE" . . "Gravitational physics"@en . . "6" . "not available" . . "Presential"@en . "FALSE" . . "Gravitational waves"@en . . "6" . "not available" . . "Presential"@en . "FALSE" . . "Mechanics of flight"@en . . "4" . "Longitudinal aerodynamic moments acting on the airplane. Longitudinal equilibrium, static stability\n and control of the airplane. Center of gravity location problem. Lateral forces and moments. Lateral equilibrium, static stability and control. Introduction into dynamics of flight: simple cases of steady and unsteady motion of the airplane. Basic natural modes of airplane (phygoid, short period, and Dutch-roll oscillations)." . . "Presential"@en . "TRUE" . . "Mechanics of flight 2"@en . . "3" . "no data" . . "Presential"@en . "TRUE" . . "Theory of relativity"@en . . "5" . "To give the student a basic understanding of the special theory of relativity and its importance for modern physics. Examples of applications\r\nof the theory are studied in the context of electromagnetism, atomic physics, high energy physics, and astrophysics." . . "Presential"@en . "FALSE" . . "Rotorcraft aeromechanics"@en . . "5" . "Principles of vertical flight, modeling and calculation of basic performance of a single rotor helicopter" . . "Presential"@en . "TRUE" . . "Computational fluid dynamics"@en . . "3" . "Knowledge about methods and tools of computational fluid dynamics." . . "Presential"@en . "TRUE" . . "Fluid dynamics applied to transport processes (5 ects)"@en . . "5" . "no data" . . "Presential"@en . "TRUE" . . "Dynamics of gravitational systems"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Extension of quantum mechanics"@en . . "6" . "Specific Competition\nCE6 - Understand the structure of matter being able to solve problems related to the interaction between matter and radiation in different energy ranges\nCE11 - Know how to use current astrophysical instrumentation (both in terrestrial and space observatories) especially that which uses the most innovative technology and know the fundamentals of the technology used\nGeneral Competencies\nCG1 - Know the advanced mathematical and numerical techniques that allow the application of Physics and Astrophysics to the solution of complex problems using simple models\nCG3 - Analyze a problem, study the possible published solutions and propose new solutions or lines of attack\nBasic skills\nCB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context\nCB7 - That students know how to apply the knowledge acquired and their ability to solve problems in new or little-known environments within broader contexts\nCB10 - That students possess the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous\nExclusive to the Structure of Matter Specialty\nCX13 - Understand in depth the basic theories that explain the structure of matter and collisions as well as the state of matter in extreme conditions\n6. Subject contents\nTheoretical and practical contents of the subject\n- Lecturers: Dr. Vicente Delgado Borges and Dr. Santiago Brouard Martín\n\n- Topics (headings):\n\n1. Approximate methods for time-dependent problems: Fermi's Golden Rule\n2. Identical Particle Systems: Second Quantization\n3. Collision Theory: Central Potentials\n4. Basic experiments: EPR, entanglement" . . "Presential"@en . "FALSE" . . "Solid mechanics materials and manufacturing."@en . . "15.00" . "NA" . . "Presential"@en . "TRUE" . . "Structural mechanics."@en . . "15.00" . "NA" . . "Presential"@en . "TRUE" . . "The finite element method in structural mechanics:"@en . . "6.00" . "The course introduces the student on the resolution of mechanical and structural problems using the Finite Element Method. The course emphasizes the formulation to understand how finite element methods work rather than black-box recipes. The course covers the formulation of finite element methods for linear-elastic problems and provides the foundation for other advanced computational mechanics courses." . . "Presential"@en . "TRUE" . . "Solid mechanics"@en . . "6.00" . "This course introduces theoretical concepts such as conservation principles, equations of movement and behaviour in material mechanics, strain and stress and elasticity, failure criteria, damage and plasticity modelling. Practical aspects are also covered including tests in mechanical laboratory, extensometry and digital image correlation and examples of engineering problems." . . "Presential"@en . "TRUE" . . "Fracture mechanics"@en . . "6.00" . "This module introduces the theoretical background to predict the failure of a structural component and describes the computational techniques that make use of these approaches in modern design." . . "Presential"@en . "TRUE" . . "Applied mechanics of materials and structures"@en . . "6.00" . "(1st and 2nd Phases): Applied examples of real and simulated cases in engineering of mechanics of materials and structures. Cases of problem solving and projects in mechanics of materials and structures in different areas: products and machinery industry, transport industry (vehicles, aerospace, etc.) and building." . . "Presential"@en . "TRUE" . . "Seminars on mechanics of materials and structures"@en . . "6.00" . "(1st and 2nd Phases): This course introduces different aspects related to the mechanics of materials and structures such as computational tools, types and selection of structural materials and experimental techniques for the mechanical characterization of structural materials. Statistical techniques and methods in mechanics of materials and structures and scientific and technical communication techniques are also covered." . . "Presential"@en . "TRUE" . . "Optimisation in engineering mechanics"@en . . "3.00" . "The course covers the main theoretical aspects on optimization: Formulation of the optimization problem; Classical (differential) methods; Modern methods: genetic algorithms, particle swarm optimization, ant colony optimization; Multiobjective optimization. Nevertheless, the approach is practical since different softwares are used to solve the optimization problems: Excel, MATLAB, ANSYS. Simple but real-life mechanical engineering problems are presented and solved in class and by the student." . . "Presential"@en . "FALSE" . . "Continuum mechanics"@en . . "4.00" . "no data" . . "Presential"@en . "FALSE" . . "Space flight mechanics"@en . . "6.00" . "Learning outcomes\nThe aim of the module is to learn basic knowledge about\n\nthe basics of space mechanics the laws of celestial mechanics\nthe time and reference systems the disruption of flight paths.\n\nThe aim of the module is to learn skills in the mathematical treatment of railway mechanical problems and in the creation of solution procedures and the programming of small solution algorithms.\n\nThe aim of the module is also to develop professional skills in space flight mechanics and in the classification of the topic Context of space technology, the development of solution approaches and the investigation of their quality.\n\nTeaching content\n\nThe content of the lecture and the exercises relate to the following topics: \nTwo-body problem \nundisturbed satellite orbits \nTime and reference systems \ngravitational and non-gravitational forces \nPerturbation theory \nspecial tracks \nRelative movement \ninterplanetary orbits \nAscent railways \nspecial problems of railway mechanics \nimpulsive railroad crossings \nSelection and application of thrust drives" . . "Presential"@en . "FALSE" . . "Mechanics"@en . . "7.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Space flight mechanics"@en . . "6.00" . "Learning Outcomes\nThe module imparts knowledge in the basics of space flight mechanics. Space system engineers need the knowledge of space flight\nmechanics for different application areas in space mission design and analysis, and orbit and attitude control of a spacecraft. The\nengineering applications of space flight mechanics include the design of satellite orbits and interplanetary trajectories, rocket ascent\ntrajectories, re-entry and landing concepts, rendezvous and docking maneuvers. Part of the outcome is the understanding of satellite orbit\ndisturbances, different types of orbits, the basic laws of celestial mechanics, and time and reference systems. Further, a focus is set on\nintroducing the programmatic aspects, thus developing the basic skills required to analyze and develop qualitative solutions for a real-life\nproblem in the relevant application areas.\nAfter successful completion of this course, students will be able to\n- describe the characteristics of orbits, time and reference systems,\n- explain the laws of celestial mechanics applicable to undisturbed satellite orbits,\n- model gravitational and non-gravitational forces acting on an orbiting spacecraft,\n- explain the influence of gravitational and non-gravitational forces on an orbiting spacecraft ,\n- apply perturbation theory to develop qualitative solutions for a real space mission analysis and design problem,\n- calculate the ground tracks using the orbital elements for a given orbit,\n- explain the principles of relative motion applicable to the field of formation flight, rendezvous and docking,\n- calculate the parameters of impulsive orbit maneuvers (e.g. delta-V, transfer time, and orbital elements),\n- explain the basics terminologies and concepts of spacecraft re-entry.\nContent\n- Two-body problem\n- Undisturbed satellite orbits\n- Time and reference systems\n- Gravitational and non-gravitational forces\n- Perturbation theory\n- Ground tracks and particular types of orbits\n- Relative motion\n- Impulsive orbit maneuvers\n- Interplanetary trajectories\n- Ascending trajectories\n- Re-entry of spacecraft\n- Applications" . . "Presential"@en . "FALSE" . . "Mechanics: laboratory practice"@en . . "4.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Advanced aerodynamics, propulsion systems and space mechanics"@en . . "no data" . "This module provides a more advanced understanding of aircraft aerodynamics and aircraft propulsion systems. It introduces advanced theories and tools for analysis of aircraft aerodynamics and also introduces aspects of the mechanics of space and orbit flight." . . "Presential"@en . "TRUE" . . "Measuring techniques in fluid mechanics"@en . . "5.00" . "no data" . . "Presential"@en . "FALSE" . . "Theoretical mechanics"@en . . "6.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Quantum mechanics"@en . . "7.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Theoretical mechanics (extended)"@en . . "8.5" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Engineering mechanics"@en . . "6.0" . "This module focuses on the physical and mathematical fundamentals on which engineering products are based on and aims to establish a firm foundation for the development of design skills and applications in the programme. The module introduces students to mathematical models of mechanical systems and simple UAV designs." . . "Presential"@en . "TRUE" . . "Fluid mechanics"@en . . "6.0" . "This module is a compilation of workshops that deliver brief introductions to tools, techniques and methodologies for aerospace engineering and UAVs. To provide a holistic view of the engineering profession the module will also focus on project management, sustainability, ethics, renewable and green energy." . . "Presential"@en . "TRUE" . . "Flight mechanics"@en . . "6.0" . "This module combines all aspects of aerodynamics, dynamics and propulsion to describe the flight physics of aircraft. The module specifically equips the students with a robust theoretical basis to formulate the equations of motion of a typical UAV configuration and will demonstrate the elementary concepts in aircraft performance, stability and flight control in flight simulation." . . "Presential"@en . "TRUE" . . "General relativity"@en . . "6.0" . "### Teaching language\n\nSuitable for English-speaking students\n\n### Objectives\n\nThe aim is to introduce the main ideas about the general theory of relativity, according to which the space-time curvature and dynamics are determined by its energy-matter content. For reach this level of understanding, the physical and mathematical principles of this formulation will be discussed. \n \nTo develop skils in theoretical physics.\n\n### Learning outcomes and competences\n\nAdquire the geometrical concepts associated to Einstein gravity, as well as the importance of this theory to describe physical phenomena.\n\n### Working method\n\nÀ distância\n\n### Program\n\n1\\. Special Relativity - Lorentz group and transformations - Vectors e Tensors - Electrodynamics 2. Einstein's Equivalence Principle - Clock Postulate and the Universality of the gravitational redshift and the geodesic deviation - Weak Equivalence Principle - Covariance under local Lorentz transformations - Covariance under position transformations - Schiff's conjecture - Princípio de Equivalência Forte 3. Generalized Covariance Principle 4. Introduction to Differential Geometry - Manifolds - Exterior derivative and Lie derivative - Covariant derivative - Curvature tensor - Metric 5. Einstein's General Relativity - Energy-Momentum tensor - Einstein's field equations - Newtonian limit, linear approximation of Einstein's field equations and gravitational waves - Matter fields - Lagrange formulation (Einstein-Hilbert action, bosonic string action and corrections to the Einstein-Hilbert action) - Classic tests: Deflection of light and radar eco delay in the vicinity of the sun, and advance precession of Mercury's perihelion 6. Exact Solutions of Einstein's field equations - Minkowski, De Sitter e anti-De Sitter space-time - Schwarzschild's black hole solution - Robertson-Walker space-time Bibliography: - S. Weinberg, \\`\\`Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity'' (John Wiley and Sons, New York 1972). Chapters: 1, 2, 3, 4, 7, 8. - S.W. Hawking and G.F.R. Ellis, \\`\\`The Large Scale Structure of Space-Time'' (Cambridge University Press, Cambridge 1973). Chapters: 1, 2, 3. - C.W. Misner, K.S. Thorne and J.A. Wheeler, \\`\\`Gravitation'' (Freeman, San Francisco, 1974). - \\`\\`300 Years of Gravitation'', Eds. S.W. Hawking and W. Israel (Cambridge University Press, Cambridge 1987). Capítulos: 4 e 5. - R.M. Wald, \\`\\`General Relativity'', (The University of Chicago Press, Chicago 1984). Chapters: 1, 2, 3, 4, 5, 6. - C.M. Will, \\`\\`Theory and experiment in gravitational physics'' (Cambridge University Press, Cambridge 1993). Capítulos: 1, 2, 3 e 14. - G.G. Ross, \\`\\`Grand Unified Theories'' (Benjamin/Cummings, Menlo Park, California 1984). Chapters: 2, 3, 4 and 12. - M.B. Green, J.H. Schwarz and E. Witten, \\`\\`Superstring Theory Vol. 1 Introduction'' (Cambridge University Press, 1987). Chapters: 2. - E.W. Kolb e M.S. Turner, \\`\\`The Early Universe'' (Addison-Wesley P. C., 1990). Chapters: 1, 3, 4, 5 and 8. - P.J.E. Peebles, D.N. Schramm, E.L. Turner e R.G. Kron, Nature, 352 (1991) 769. - O. Bertolami, \\`\\`Modelo Cosmológico Padrão: uma breve introdução'', \"Agregação\" lecture, Instituto Superior Técnico, July 1996.\n\n### Mandatory literature\n\nSchutz Bernard F.; [A first course in general relativity](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000224998 \"A first course in general relativity (Opens in a new window)\"). ISBN: 0-521-25770-0 \n\n### Complementary Bibliography\n\nHawking Stephen 1942-2018; [The large scale structure of space-time](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000233043 \"The large scale structure of space-time (Opens in a new window)\"). ISBN: 0521200164 \nS. Weinberg; Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity \nWeinberg Steven; [Gravitation and cosmology](http://catalogo.up.pt/F/-?func=find-b&local_base=FCUP&find_code=SYS&request=000238852 \"Gravitation and cosmology (Opens in a new window)\"). ISBN: 0-471-92567-5 \n\n### Teaching methods and learning activities\n\nTheory and problem solving lectures.\n\n### Evaluation Type\n\nDistributed evaluation with final exam\n\n### Assessment Components\n\nExam: 75,00%\nWritten assignment: 25,00%\n\n**Total:**: 100,00%\n\n### Amount of time allocated to each course unit\n\nDevelopment of report/dissertation/thesis: 30,00 hours\nAutonomous study: 90,00 hours\nFrequency of lectures: 42,00 hours\n\n**Total:**: 162,00 hours\n\n### Eligibility for exams\n\nAttendance of theoretical/pratical lectures.\n\n### Calculation formula of final grade\n\nThe final mark has a 75% component from the exam and a component of 25% from a written essay also presented orally. The minimum grading for the exam is 8.\n\n### Classification improvement\n\nSecond examination round for the exam mark (75% of the total mark).\n\nMore information at: https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509988" . . "Presential"@en . "TRUE" . . "Advanced quantum mechanics"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509346" . . "Presential"@en . "FALSE" . . "Spaceflight mechanics"@en . . "9.0" . "The course aims at developing the fundamental engineering aspects of orbital and attitude dynamics of rigid spacecraft, starting from ideal conditions (Keplerian motion and free-spinning spacecraft), then including relevant practical aspects, such as the effects of perturbing and control force and torques, up to the determination of control and maneuver strategies in response of mission requirements. At the end of the course, the student is expected 1) to understand the most relevant aspects of spacecraft dynamic behavior; 2) to solve problems which requires the determination of orbit features, orbital maneuvers or characterize attitude motion of a rigid spacecraft." . . "Presential"@en . "TRUE" . . "Geophysical and astrophysical fluid dynamics"@en . . "6.0" . "Fluid mechanics of the Earth and planets, including oceans, atmospheres and interiors, and the fluid mechanics of the sun. In addition, their magneto-hydrodynamic behaviors are investigated." . . "Presential"@en . "TRUE" . . "Microgravity flows"@en . . "6.0" . "Before entering the master of science program, aerospace engineers are already acquainted with the basic principles of fluid motion being trained on fundamental aspects of aerodynamics and gas dynamics. This level of knowledge is however deeply insufficient to understand how, even ordinary, fluids, such as air and water, behave in low gravity. The reduced weight adds indeed to the complexity of fluid behavior and enhances the effects of forces like surface tension that are usually negligible at the human scale on the Earth. In addition to that, the long permanence in the restricted environment of the spaceship, or, respectively, inside habitation modules, requires confidence with the more complex physiological fluids, and an understanding of how rheologically exotic fluids may behave.\n\nIn this framework, the course in microgravity flows is dedicated to providing the students interested in the microgravity environment with the appropriate tools to understand and design fluidic applications for and in the context of space sciences. The overall purpose is to train the students to identify the challenges posed by fluid motions in space systems and to propose effective solutions to problems involving their dynamics in the context of payload design, onboard systems, and manned missions.\nIn this context, the following educational objectives are envisioned for the course in Microgravity Flows.\nKnowledge:\n- Provide the students with a basic understanding of the equations governing fluid motion starting from basic principles, leading them to master the most fundamental models of fluid rheology, surface effects, and the processes of phase change in fluids under microgravity.\n- Introduce the student to the behavior of soft materials and physiological fluids, with emphasis on hemodynamics and the lymphatic system and their response to the low gravity environment.\n- Understand the effect of fluid motion on the dynamics of a spacecraft.\nKnow-how:\n- Capacity to identify the relevant model to describe different kinds of fluid motions in microgravity and understand the relevant application context.\n- Capacity to conceive basic microfluidic systems and define the fabrication procedure at the prototypal level.\n- Capacity to translate the mathematical models of fluid motion into computational algorithms.\n- Capacity to perform numerical simulations and interpret the results.\n- Define the main characteristics of an experiment involving fluids in microgravity, select the most appropriate platform for its realization, and interpret the data.\nSoft skills:\n- Ability to produce a report concerning technical aspects of fluid motion in the space environment.\n- Ability to actively work in a team and contribute ideas to a given project.\n- Ability to publicly discuss and explain aspects related to fluid motion in low gravity to both technical and general audiences." . . "Presential"@en . "TRUE" . . "Mechanics and waves"@en . . "6.0" . "Prerequisites\nDifferential and Integral Calculus I and II\n\nObjectives\nGeneral: Quantitatively predict the consequences of a variety of physical phenomena with calculatory tools. Ensure advanced and thorough scientific training in a fundamental field of Physics, hence allowing for disciplinary or interdisciplinary approaches to innovation. Specific: Ability to understand and interconnect the concepts and basic principles of classical Mechanics and Waves, such as mass, energy, work, oscilations and waves, through an integrative perspective; ability to apply them to problem solving, particularly in what concerns their technological applications.\n\nProgram\n1.Kinematics: position, velocity and acceleration vectors; rectilinear and circular motions. 2.Forces and frames: relative motion; inertia principle; conservation laws and space-time symmetries. 3.Work and energy: kinetic energy; conservative forces; potential and mechanical energies; energy conservation and time invariance. 4. Linear momentum: particle system and center of mass; conservation of linear momentum and translation invariance; collisions. 5. Angular momentum and torque: torque; equilibrium conditions. 6.Gravitation: Kepler's laws and central forces; conservation of angular momentum and space isotropy. 7. Rigid body: moment of inertia; static; translation and rotation; gyroscope. 8.Ocillations: simple harmonic, damped and forced; resonance. 9.Waves: sinusoidal and characteristic parameters; transverse and longitudinal, stationary (vibrating rope); plane and spherical waves; beats; Huyguens principle; reflection, refraction and dispersion; interference and diffraction.\n\nEvaluation Methodology\n50% continuous assessment by Mini-tests (exclusively during class hours) [If an appropriate number of graders and/or teaching assistants is available, oral presentations and/or solution discussions can be considered] 50% Exam\n\nCross-Competence Component\nThe CU promotes, through exposure to its themes and practical problem solving, the skills of Critical and innovative thinking [Problem solving strategies, Strategic thinking, Critical thinking, Creativity] as well as Intrapersonal skills [Intrinsic motivation, Productivity and time management]. Interpersonal skills in Written communication and Information literacy in document structuring may weigh up to 5% in written assessments.\n\nLaboratorial Component\nNone\n\nProgramming and Computing Component\nNone\n\nMore information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938490001" . . "Presential"@en . "TRUE" . . "Advanced general relativity"@en . . "6.0" . "Learning objectives\n\nReferring to knowledge\n\nBecome familiar with advanced techniques in general relativity applied to the study of black holes and relativistic cosmology, including inflationary theory and structure formation in the universe. Classical theory in both contexts is discussed in detail and an introduction to quantum aspects is provided. \n\nTeaching blocks\n\n1. Mathematical background\n2. General formalism\n2.1. Lagrangian formulation\n\n2.2. Causal structure and conformal diagrams\n\n3. Classical theory of black holes\n3.1. General analysis and theorems\n\n3.2. Charged and rotating black holes\n\n4. Quantum fields in curved spacetime; Hawking radiation\n5. Black hole thermodynamics; Information paradox\n6. Basic notions in the quantum theory of gravity\n7. Relativistic cosmology; Causal structure of FRW universes\n8. Cosmological perturbation theory\n8.1. Formalism\n\n8.2. Transfer functions\n\n8.3. CMB and matter power spectrum\n\n9. Inflation as the origin of primordial perturbations; Predictions and observations\n \n\n \n\nTeaching methods and general organization\n\n \n\nFace-to-face sessions, in which lecturers present the theoretical aspects of the course. Students solve weekly set exercises individually.\n\n \n\n \n\nOfficial assessment of learning outcomes\n\n \n\nContinuous assessment consists of exercises solved weekly by students.\n\n \n\nExamination-based assessment\n\nStudents are entitled to single assessment only if they are unable to meet the requirements for continuous assessment.\n\nRepeat assessment takes place in September and consists of an examination.\n\n \n\n \n\nReading and study resources\n\nCheck availability in Cercabib\n\nBook\n\nPoisson, Eric, A Relativist’s Toolkit. Cambridge University Press (2009) https://doi.org/10.1017/CBO9780511606601\n\nhttps://cercabib.ub.edu/permalink/34CSUC_UB/18sfiok/alma991004393639706708 Enllaç\n\nWald, Robert M. General relativity. Chicago : The University of Chicago Press, 1984 Enllaç\n\n\nCarroll, Sean M. Spacetime and geometry : an introduction to general relativity. New intern. ed. Essex :Pearson, 2014 Enllaç\n\n\nhttps://cercabib.ub.edu/discovery/search?vid=34CSUC_UB:VU1&search_scope=MyInst_and_CI&query=any,contains,b1751678* Enllaç\n\nHawking, S. W. ; Ellis, George Francis Rayner. The large scale structure of space-time. Cambridge : Cambridge University Press, 1973 Enllaç\n\n\nChandrasekhar, S. The Mathematical theory of black holes. New York : Oxford University Press, 1992 Enllaç\n\n\nKolb, Edward W. ; Turner, Michael S. The early universe. Reading : Addison-Wesley, 1990 Enllaç\n\n\nLiddle, Andrew R. ; Lyth, D. H. Cosmological inflation and large-scale structure. Cambridge : Cambridge University Press, 2000 Enllaç\n\n\nMukhanov, V. F. Physical Foundations of Cosmology. Cambridge : Cambridge University Press, 2005 Enllaç\n\n\nElectronic text\n\nPoisson, E., An Advanced Course in General Relativity Enllaç\n\n\nHartman, T., Lectures on Quantum Gravity and Black Holes Enllaç\n\n\nTownsend, P. K., Black Hole lectures @ DAMTP Enllaç\n\n\n\nMore information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568435&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "FALSE" . . "General relativity"@en . . "6.0" . "http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=569107&ens=M0D0G&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "FALSE" . . "Experimental physics I: classical mechanics and thermodynamics"@en . . "8" . "no data" . . "Presential"@en . "TRUE" . . "Experimental physics II: optics, electromagnetism and relativity"@en . . "8" . "no data" . . "Presential"@en . "TRUE" . . "Experimental physics III: quantum mechanics, atomic physics and nuclear physics"@en . . "8" . "no data" . . "Presential"@en . "TRUE" . . "Theoretical physics I: classical mechanics"@en . . "9" . "no data" . . "Presential"@en . "TRUE" . . "Theoretical physics III: quantum mechanics"@en . . "9" . "no data" . . "Presential"@en . "TRUE" . . "Engineering mechanics-statics"@en . . "5" . "no data" . . "Presential"@en . "TRUE" . . "Soil mechanics"@en . . "5" . "Nature and properties of soils. Categorization and classification schemes. Ground water and its influence on its mechanical behaviour. Mechanical behaviour of soils. Calculation of stresses in the soil. Deformation of soil. Settlement of soil. Time-dependent behaviour (creep). Lateral pressure of soils. Bearing capacity of surface foundations. Stability of slopes. Slope failures. The course consists of laboratory sessions." . . "Presential"@en . "TRUE" . . "Computational fluid dynamics"@en . . "6" . "Not provided" . . "Presential"@en . "FALSE" . . "Structural mechanics of aircraft structures"@en . . "4" . "Not provided" . . "Presential"@en . "FALSE" . . "Classical Mechanics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .