Syllabus

1. Review of Newton’s equations of motion. Constraints and how to deal with them.

2. Lagrangian Mechanics. Degrees of freedom. Generalized coordinates. Variational Calculus. What is an inertial frame of reference? Galilean Invariance. Derivation of Newton’s first and second laws.

3. Symmetries and Conservation Laws. Derivation of Newton’s third law. Reciprocity and its violation. Mechanical similarity. Virial theorem

4. Conservation of linear momentum. The two-body problem.

5. Conservation of angular momentum. The central force problem. Kepler’s laws.

6. Scattering in a potential.

7. Small Oscillations. Oscillation in 1D. Oscillation in higher dimensions. Normal modes. Vibration of molecules. Damped Oscillation. Parametric resonance. Anharmonic oscillation. Resonance in nonlinear oscillation. Motion in a rapidly oscillating field.

8. Rigid body dynamics.

9. Hamiltonian Mechanics. Noether’s theorem.

10. Hamilton Jacobi theory.

11. Canonical transformations.

12. Nonlinear dynamics. Fixed points. Linear stability analysis. Jacobian. Attractors. Bifurcation. Chaos.

Recommended Texts

•  Rana and Joag, Classical Mechanics, McGraw Hill.

• Landau and Lifshitz, Mechanics.

Other Texts

• Goldstein, Poole, Safko - Classical Mechanics.

Detailed readings are on the page: PH 201 Classical Mechanics, August 2024 – Sumantra Sarkar Group.

Similar Courses

• Theoretical Mechanics, IIT Guwahati by Dr. Charudatt Y. Kadolkar - https://nptel.ac.in/courses/115103115.

• Topics in Nonlinear Dynamics, IIT Madras by Prof. V. Balakrishnan - https://nptel.ac.in/courses/115106059.

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