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

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

References

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