PHYUT501 CLASSICAL MECHANICS
Constraints, Classification of Constraints, Principal of Virtual Work, D’Alembert’s
principal and its applications (Problems only), (One or Two Problems should be discussed
with D’Alembert’s, Lagrangian, Hamiltons from same set of problems).
Generalized coordinates, Langrange’s equations of motion, properties of kinetic
function, theorem on total energy, generalized momenta, cyclic-coordinates, integrals
of motion, Jacobi integrals and energy conservation, Concept of symmetry, invariance under
Galilean transformation, velocity dependent potential.
Hamilton’s function and Hamilton’s equation of motion, configuration space, phase
space and state space, Lagrangian and Hamiltonian of relativistic particles and light rays.
Variational principle, Euler’s equation, applications of variational principle, shortest
distance problem, brachistrochrone, Geodesics of a Sphere.
Generating function, Conditions for canonical transformation and problem.
Definition, Identities, Poisson theorem, Jacobi-Poisson theorem, Jacobi identity,
(statement only), invariance of PB under canonical transformation.
Rotating frames of reference, inertial forces in rotating frames, Larmour precision,
electromagnetic analogy of inertial forces, effects of Coriolis force, Focoult’s pendulum.
Two body central force problem, stability of orbits, condition for closure, integrable
power laws, Kepler’s problems, orbits of artificial satellites, Virial theorem.