Physics 601: A Modern Treatment of Classical Mechanics
This course re-examines and develops the laws of the Newtonian Universe in the light of the developments of 20th century science. Before Einstein, Newton developed the concepts of Galilean relativity and the invariance of physical laws. The development of canonical transformation theory in the last century laid the foundation for describing the laws of nature in term of symmetry principles. The correspondence of classical and quantum mechanical observables is explored. Covered as well is the connection between Hamilton-Jacoby theory to the ray optics limit of wave mechanics. Action-angle formulation of maps is used to introduce perturbation theory and chaotic systems. This classical theory is generalized to Einstein's restricted theory of special relativity in 4 dimensional space-time.
MWF: 11:00 AM-12:20 PM
(Includes Problem Session)
Syllabus
- Newton's legacy: space, time, motion, inertia, and the implicit stability of elementary matter.
- Extremum principles and the motion of physical systems.
- Formal invariance of physical laws.
- Lagrangian and Hamiltonian dynamics.
- Rotational dynamics of rigid bodies.
- Small Oscillations.
- Canonical transformations, classical observables, Poisson brackets, and the connection to quantum mechanics.
- Hamilton-Jacoby theory, action-angle variables.
- Maps and Chaos.
- Special Relativity