Course Code:

422511
Course Outline:

**Overview and Objectives:**

This course is designed to provide the students with a solid understanding of the fundamental aspects of classical mechanics which is a core part in physicist's education. The main goal is to prepare the students for the study of modern physics. The advanced formulations of classical mechanics serve as the basis of various branches of physics. The student will be able to: 1. Set up Lagrangian and solve Lagrange's equations, 2. Treat central forces, 3. Treat rigid body motion, 4. Investigate small oscillations, 5. Set up the Hamiltonian and Hamilton's equations.

*Material:*

- Newtonian mechanics of a particle and system of particles, D'Alembert's Principle and Lagrange's equations, Dissipation function, Applications of the lagrangian.
- Hamilton's Principle, Calculus of variation, Euler-Lagrange differential equations. Lagrange multipliers and conserved quantities.
- Two-body central forces and the one-body 1D equivalent, Classification of orbits, Virial theorem, orbit shapes and Bertrand's theorem, the Kepler Problem.
- Rotations of a rigid body, Euler angles, infinitesimal rotations, time derivatives in rotating frames.
- Inertia tensor and moments of inertia, Principal moments and Principal axes, Euler equations of motion.
- Small oscillations: Normal coordinates and normal modes, free vibrations of linear triatomic molecule, forced vibrations and dissipation.
- Hamilton's equations of motion and conservation theorems, Variational Principle and the Hamiltonian.

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