Learning objective: To introduce the student to various aspects of Classical Dynamics Learning outcomes: After the student completes this course he/she will be familiar with aspects of Classical Mechanics such as Lagrangian and Hamiltonian formulation, particle in central potentials, rigid body motion, integrable and non-integrable systems and special relativity. These will form the essential background for other courses such as Quantum Mechanics, Electrodynamics, Classical and Quantum Field Theory, High Energy Physics and General Relativity that the student would learn in the subsequent semesters
Lagrangian formulation: Degrees of freedom, constraints, generalized coordinates and velocities, Lagrangian, Euler-Lagrange equation, examples. Symmetries and conservation laws: Conservation of momentum, angular momentum and energy, virial theorem Central force motion: Kepler problem, Scattering in a central potential, Rutherford formula. Small oscillations: Perturbations away from equilibrium, stability analysis, normal modes and normal coordinates, examples (molecular dynamics). Rigid body motion: Motion in non-inertial frames, Coriolis force, degrees of freedom of a rigid body, moment of inertia tensor, principal axes, Euler angles and Euler equations of motion, example (symmetric top). Hamiltonian formalism: Legendre transforms, generalized momenta, Hamiltonian, Hamilton's equations, phase space and phase trajectories, examples, conservative versus dissipative systems (simple examples). Canonical transformations: Poisson brackets, Louiville's theorem, Generating functions, Action-angle variables Elements of time-independent perturbation theory, introduction to non-integrable systems. Special relativity: Postulates of relativity, Lorentz transformations, length contraction and time dilation, Doppler effect,velocity addition law, four-vector notation.
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2. H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Third Edition (Pearson Education, India, 2002).
3. Jorge V. Jose, and Eugene J. Saletan, Classical Dynamics, A contemporary approach, Cambridge Univ. Press, 1998.
4. OL. De Lange, and J. Pierrus, Solved Problems in Classical Mechanics: Analytical and numerical solutions with comments, Oxford University Press, 2010.
5. David Morin, Introduction to Classical Mechanics, with problems and solutions, Cambridge Univ. Press, 2008.
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8. E. F. Taylor and J. A. Wheeler, Spacetime Physics (W. H. Freeman, San Francisco, 1992).
9. D.S. Lemons, Perfect Form (Princeton U. Press, 1997)