**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Lagrangian formulation of mechanics. Degrees of freedom and equations of motion. Constraints and Generalized coordinates. Principle of least action. Emphasis on the Variational principle. The Calculus of Variations. Euler-Lagrange equations. Constrained systems and Lagrange multipliers.
- Phase space formulation. Hamiltonian, phase space, Poisson brackets. Canonical transformations. Liouville's theorem and Poincare recurrence. Hamilton-Jacobi theory. Action-angle variables.
- Oscillators. Small fluctuations. Damped,forced and anharmonic. Eigenvalue equation and principle axis transformation, normal coordinates, forced oscillations and resonance, vibrations of molecules. Nonlinear oscillations and chaos.
- Motion in a central field. Equivalent one-body problem. first integrals, classification of orbits, virial theorem, Bertrand's theorem Kepler's law. Symmetries and conservations laws. Noether's theorem. Central forces in three dimensions. Scattering in a central force field, Rutherford scattering.
- Rigid bodies. Rotation. Orthogonal transformations, Euler angles, rigid body dynamics, spinning top.

- H. Goldstein, C. P. Poole and J. L. Safko, Classical mechanics, 03rd edition, Addison-Wesley (2001).
- L. D. Landau and E. M. Lifshitz, Mechanics, 03rd edition, Butterworth Heinemann (1976).
- N. C. Rana and P. S. Joag, Classical Mechanics, Tata McGrawHill (1992).
- V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics, 03rd edition, Springer (2006).
- J. V. Jose and E. J. Saletan, Classical dynamics: a contemporary approach, Cambridge University Press (1998).
- W. Greiner, Classical Mechanics - Systems of Particles and Hamiltonian Dynamics, Springer (2002).