Modern theoretical mechanics 1102-4FT14

Following topics will be discussed

- Lagrange equations of motion:
generalized coordinates
Stationary Action Principle
Galillean invariance
- motion in one dimension and in central field of force
one dimensional motion in a potential
friction
Center of Mass and Jacobi coordinates
motion in a central field
Kepler problem
- small oscillations and Finite Fourier Transform
small oscillations
eigenfrequencies, degeneration
systems possessing finite dispalecment symmetry
Finite Fourier Transform, waves in one dimensional crystal
- Symmetries and Emma Noether Theorem
conservation laws
Emma Noether Theorem
- Motion of a solid
angular velocity, inertial tensor
Euler equarions
equations of motion in a noninertial frame
- Deterministic Chaos
logistic equation, bifurcations, atractors
chaotic pendulun, Lyapunov exponents
3 body problem
- Cannonical equations: Hamilton & Hamilton-Jacobi
Hamilton equation
Poisson brackets
Maupertuis principle
Liouvilee theorem
Hamilton-Jacobi equations
variable separation
- Relativistic Mechanics
interval, Lorentz transformation
constant acceleration motion
Action for a relativistic particle
Action in external electromagnetic field, Lorentz force

- Black Hole:particles and light in Schwartzschild metric
metric in 3 dimentional space
Schwartzschield metric,absolute time, interpretation
Hamilton-Jacobi equation for a free particle
massive particle, perilelion precession
foton
falling into a black hole: a tale of two descriptios,
by the hapless victim and by far away observer

Time permiting, I will treat classical scattering theory