Review of Newtonian Mechanics:

Frame of reference, orthogonal transformations, angular velocity and angular acceleration, Newton’s laws of motion,  Galilean  transformation, conservation laws,  systems  of  particles, motion under a constant force, motions under variable force, time-varying mass system.

The Lagrange Formulation of Mechanics and Hamilton Dynamics:

Generalized co-ordinates and constraints, D’Alembert’s principle and Lagrange’s Equations, Hamilton’s principle, integrals of motion, non conservative system and generalized potential, Lagrange’s multiplier method,
the  Hamiltonian  of  a  dynamical  system,  canonical  equations,  canonical
transformations, Poisson brackets, phase space and Liouville’s theorem.
Central Force Motion: The two-body problem, effective potential and classification of orbits, Kepler’s laws, stability of circular orbits, hyperbolic orbits and Rutherford scattering, center of mass co-ordinate system, scattering cross-sections.
Motion in Non-inertial Systems: Accelerated translational co-ordinate system, dynamics in rotating co-ordinate system, motion of a particle near the surface of the earth.
The Motion of Rigid Bodies: The Euler angles, rotational kinetic energy and angular momentum, the inertia tensor, Euler equations of motion, motion of a torque-free symmetrical top, stability of rotational motion.