## PHY 301: Classical Mechanics

3 credits | Prerequisites: PHY 101, 222, 223 for Major; PHY 230 for Minor

### Course rationale

The goal of this class is primarily to give you a different perspective on the Newtonian classical mechanics that you should be familiar with from school and/or freshman year. To this end, the course reformulates mechanics in terms of objects called Lagrangians and Hamiltonians using calculus of variations.

### Course content

Coordinate Systems and Transformation: Cartesian coordinates; circular cylindrical coordinates; spherical coordinates, Centre of mass and linear momentum of a system, Angular momentum and kinetic energy of a system, Motion of two interacting bodies. Some Methods in the Calculus of Variations: Euler’s equation, the second form of the Euler equation, functions with several dependent variables, Euler’s equation when auxiliary conditions are imposed, Rotation about an arbitrary axis, Principal axes of a rigid body. Lagrangian & Hamiltonian Mechanics: Hamiltonian’s principle, generalized coordinates, Lagrange’s equations of motion in generalized coordinates, Lagrange’s equations with undetermined multipliers, a theorem concerning the kinetic energy, conservation theorems, canonical equations of motion – Hamiltonian mechanics. Central Force Motion: reduced mass, conservation theorems-first integrals of the motion, planetary motion- Kepler’s problem. Motion in a non-inertial reference: frame: rotating coordinate systems, centrifugal and Coriolis forces, motion relative to the earth. Mechanics of rigid Bodies: inertia tensor, angular momentum, principal axes of inertia, moments of inertia for different body coordinate systems, Eulerian angles, Euler’s equations for a rigid body, Collision theory: The Scattering Angle and Impact Parameter, The Collision Cross Section, Generalizations of the Cross Section, The Differential Scattering Cross Section, Calculating the Differential Cross Section.

### Course objectives

- How to solve hard problems with relative ease through Lagrangian Mechanics.
- The theoretical foundation for advanced physics using Hamiltonian Mechanics.
- Understand the notions of configuration space and generalized coordinates space in mechanics.

### References

- Landau, Lev D., and Evgenij M. Lifshitz. Mechanics: Course of Theoretical Physics. Vol. 1. Butterworth Heinemann, 1976. ISBN: 9780750628969.
- John R. Taylor, Classical Mechanics, ISBN 978-1-891389-22-1.
- Goldstein, Poole, & Safko, Classical Mechanics, 3rd Edition.