PH4030: Classical Mechanics (3-1-0-8)

D’Alembert’s principle and Lagrange equation: Generalized coordinates, principle of virtual work, D’Alembert’s principle, Lagrangian formulation and simple applications.

Variational principle and Lagrange equation: Hamilton’s principle, Lagrange equation from Hamilton’s principle, Extension to non-Holonomic systems, Lagrange multipliers, symmetry and con-servation laws.

Hamiltonian formulation: Legendre transformations, Hamilton’s equations, symmetries and conser-vation laws in Hamiltonian picture, Hamilton’s principle, canonical transformations, Poisson brackets, HamiltonJacobi theory, action-angle variables.

Central force problem: Two body problem in central force, Equations of motion, effective potential energy, nature of orbits, Virial theorem, Kepler’s problem, condition for closure of orbits, scattering in a central force field, centre of mass and laboratory frame.

Rotating frame: Angular velocity, Lagrange equation of motion, inertial forces.

Rigid body motion: kinetic energy, momentum of inertia tensor; angular momentum, Euler angles, heavy symmetrical top, Euler equations, stability conditions.

Small Oscillations: Eigenvalue problem, frequencies of free vibrations and normal modes, forced vibrations, dissipation

Texts:

1. (to be informed in the class).