**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.

**M****otion 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.