Classical and celestial mechanics 0800-PA-CELMECH

The topics covered by the course include:

1) The fundamental concepts of Newtonian mechanics, gravitational potential outside uniform sphere (spheroid) and due to uniform disk (ring), generalized coordinates, basics of Lagrangian and Hamiltonian 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 problem and the equations of motion in relative coordinates, Jacobi 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). Examples: simple models of motion in galactic gravitational environments (such as the Henon-Heiles model), Sitnikov problem.

5) 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.

6) 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.