Syllabus
* A brief historical overview.
* A brief overview of analytical mechanics:
Lagrange and Hamiltonian approach; Lagrange equations of the second kind; Hamilton equations; canonical transformations; Poisson and Lagrange brackets; symplectic matrix; Hamilton-Jacobi equation; particle in one-diemnsional potential.
* Two-body problem:
Basic formulation; transformation of barycenter; relative coordinate; momentum and angular momentum integrals; Binet equation; Kepler equation and variants for parabolic and hyperobolic motions; orbital and non-singular orbital elements; solution of the two-body problem using Hamilton-Jacobi equation; Delaunay variables; elliptic expansions (Bessel functions; Hansen functions).
* Circular restricted problem of three bodies:
Equations of motion in the inertial and synodic reference systems; Jacobi integral; Tisserand criterion; Hill's planes of zero velocity; stationary solutions (Lagrange points); stability of stationary solutions.
* Elliptic restricted problem of three bodies:
Nechvile's transformation to rotating and pulsating coordinate system; non-integrability; stationary solutions and their stability;
* Hill's problem:
Jacobi coordinates; equations of motion in synodic reference system; Hill's surfaces of zero velocity; lunar origin; theory of lunar motion; variational solution.
Annotation
Motion in gravitational field, recapitulation of elements of analytical mechanics. Two-body problem.
Three-body problem in two approximations: (i) restricted problem, and (ii) Hill's problem. For students of the first year of master studies in astronomy.