Classical Mechanics E 1100-2Ind02

The classical mechanics, besides solving its characteristic physical problems, is the place, where there appear the basic physical notions, entering into other branches of physics. In the first scope, the lecture is the continuation and development of the former "Basic Physics I (Mechanics)", the large part of it is however conceived to serve as brief introduction to Quantum Mechanics, Electrodynamics and Relativistic Gravitation.

Program:
1. Brief introduction to variational calculus. Newton equations with potential forces as equations of a variational principle. Extension to arbitrary coordinates and to systems with holonomic constraints. Examples.
2. Small oscillations of mechanical systems. Normal coordinates. Transition to the limit of infinite number of degrees of freedom.
3. Descriptions of a rigid body configurations. Euler equations. The lagrangian of a symmetrical top. Gyroscope on the rotating Earth. Action in a magnetic field. The vector potential. Charged symmetrical top in the homogenous magnetic field.
4. Symmetry and the conservation laws. Noether theorem. The group of Galileo and Lorentz. Relation among them. Relativistic action.
5. The variational Principle in the phase space. Hamilton equations. Liouville's theorem.
6. The Jacoby variational principle in classical and relativistic mechanics, including relativistic gravity of Einstein.
7. The canonical transformations. The Hamilton - Jacoby equation. Separation of variables in the H-J equation. Action integral along the physical trajectory as the solution of H-J eq. Action as the phase of a "wave". Motion of wave packets. Quantisation conditions. Equation for Exp[iS/h]. The Schroedinger equation.
8. Basic equations of hydrodynamics.
9. Deterministic chaos

Description by Andrzej Szymacha, February 2009,
modified by Janusz Rosiek, August 2013, new version Krzysztof Meissner 2023