Classical Mechanics Mock Papers

Compilation of semester exam level questions in Classical Mechanics on following topics. VARIATIONAL CALCULUS - Euler equation, Lagrange multipliers, Holonomic and Non-holonomic constraints. LAGRANGIAN MECHANICS - degrees of freedom, virtual work, generalised coordinates, velocities and forces, conservative Lagrangian and Hamiltonian. SMALL VIBRATIONS - double pendulum, kinetic and potential energy matrices, Normal modes and frequencies, superimposition of different modes, linear triatomic molecule, point masses connected by string. CENTRAL FORCES - Quadratures, centre of mass frame, effective potential, gravitational attraction and Kepler problem, circular and elliptical closed orbits, parabolic and hyperbolic open trajectories, repulsive forces and orbits/trajectories. HAMILTONIAN DYNAMICS - rotational invariance and angular momentum conservation, Noether’s Theorem, Legendre transformation, Hamilton’s equations of motion, Liouville’s theorem, Momentum space. THEORETICAL MECHANICS - Canonical transformations, three forms of generating function, Poisson brackets. ROTATING SYSTEMS - infinitesimal and finite 3D rotations, rotated and rotating reference frames, angular velocity, fictitious forces. RIGID BODY DYNAMICS - moment of inertia tensor, kinetic energy and angular momentum, Euler equation for force-free motion, motion of torque-free symmetric top, Euler angles, motion of heavy symmetric top.