. "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" .