Analytical Mechanics -- Fall 2006
| Material covered: |
| Week | Monday | Wednesday |
| Oct 30 | Rotational motion of rigid bodies:
General properties of rotations |
Rotational motion of rigid bodies:
Kinetic energy, moments of inertia |
| Nov 06 | Rotational motion of rigid bodies:
Angular momentum and its dynamics |
Rotational motion of rigid bodies:
Euler angles; Symmetric top |
| Nov 13 | Rotational motion of rigid bodies:
Euler equation; Asymmetric top (qualitatively) |
Systems with constraints:
Holonomic, nonholonomic, etc. Variational principle with constraints d'Alembert's principle |
| Nov 20 | Hamiltonian formalism:
Hamiltonian function and equations, Variational principle; Poisson Brackets |
Thanksgiving |
| Nov 27 | Hamiltonian formalism:
Canonical transformations |
Hamiltonian formalism:
Action as a function of coordinates |
| Dec 04 | Hamiltonian formalism:
Hamilton-Jacoby equation |
Hamiltonian formalism:
Integrable and nonintegrable systems Dynamical chaos |
| Dec 11 | Hamiltonian formalism:
Angle-action variables and adiabatic invariant |
Hamiltonian formalism:
Parametric resonance via natural and angle-action variables |
| Weekly problem sets:
|
| Oct 30 | Nov 06 | Nov 13 | Nov 27 | Exam 2 (Dec 18) |
| Set 1 | Set 2 | Set 3 | Set 4 | Problems |
| Additional materials, with Wolfram Mathematica program
files (M) and archive files (A) (if you do not have Mathematica, you still can view the programs using the freeware Mathreader)
|
| 1. Dmitry Garanin,
Classical Mechanics 2. Landau and Lifshitz, Mechanics 3. David Tong, Lectures on Classical Dynamics |