Analytical Mechanics -- Fall 2008
| Material covered: |
(Syllabus) (see also Analytical Mechanics -- Fall 2006, Fall 2007) |
| Week | Monday | Wednesday |
| Nov 03 | . | 
Rotational motion of rigid bodies:
Kinematics of rotations. Large and small rotations. Angular velocity, centripetal acceleration. Rolling constraint. Rotation matrices. Euler angles |
| Nov 10 | Rotational motion of rigid bodies: Dynamics of rotations Kinetic energy, moments of inertia. Angular momentum in the laboratory and body frames. Equation of motion for the angular momentum. Free symmetric top. |
Rotational motion of rigid bodies: Equations of motion for the Euler angles of a free asymmetric top. Larmor equation for a rapidly rotating top. Problems on rotational energy |
| Nov 17 | Rotational motion of rigid bodies: Lagrange formalism: Heavy symmetric top. |
Rotational motion of rigid bodies: Newtonian formalism: Euler equations. Free asymmetric top. Wheel rolling on a plane  |
| Nov 24 | Hamiltonian
mechanics: Hamiltonian function and equations, Variational principle; Poisson brackets |
Hamiltonian mechanics: Canonical transformations |
| Dec 01 | Hamiltonian mechanics: Action as a function of coordinates. Hamilton-Jacoby equation. Free particle and harmonic oscillator. |
Hamiltonian mechanics: Separation of variables in the Hamilton-Jacoby equation. Particle in spherical coordinates. |
| Dec 08 | Hamiltonian mechanics: Angle-action variables. Adiabatic invariants |
Parametric resonance |
| Dec 15 |
Dynamical chaos |
| Weekly problem sets: |
| Nov 10 | Nov 17 | Dec 01 | Exam 2 |
| Set 1 | Set 2 | Set 3 | |
| Solution | Solution | Solution 1,2 Solution 3 |
| 1. Dmitry Garanin,
Classical Mechanics 2. Landau and Lifshitz, Mechanics 3. David Tong, Lectures on Classical Dynamics |
| Heavy wheel rolling on a plane without slipping and with no horizontal force. This is only one of many different types of motion - the so-called "drunk wheel" that does not have enough spin to support steady motion. The trajectory of the center is shown in black and that of the contact point in red. Note that here the direction of the wheel's precession changes with time. |