| Week | Chapter | Mon | Wed | Fri | Homework |
| 1 - Aug 28 - Sep 1 |
1-Elementary Principles | Introduction 1.1 Mechanics of a particle |
1.2-1.3 Systems of particles |
1.4 Constraints Example: double pendulum |
Hwk#1, Ch1: 1, 4, 5, 13, 14 (due Thu Sep 7, 5pm) Solutions |
| 2 - Sep 4 - Sep 8 |
1-Elementary Principles |
Labor Day | 1.4-1.5 D'Alembert's principle, Lagrange's equations Example: pendulum with a moving support. |
1.5-1.6 Velocity-Dependent Potential, Dissipation function. 2.6-7 Energy function |
Hwk#2, Ch 1: 9, 15(a,b), 19, 21, 23, 24(a,b) (due Thu Sep 18, 11:30am) Solutions Useful formulae for spherical coordiantes. |
| 3 - Sep 11 - Sep 15 |
2-Variational Principles | 2.1-3 Hamilton's principle, Brachistochrone problem |
2.2-5-6 Conservation Theorems Noether's theorem Emmy Noether's biography |
2.3-4 Lagrange's equations with constraints |
Hwk #3, Ch2: 4, 14, 18, 19, 20, 21(a,b) (due Wed Sep 27, 11:30am) Solutions |
| 4 - Sep 18 - Sep 22 |
2-Lagrange's equations 3- Central Force Problem |
2.4-5 Lagrange's equations with constraints Example: Two wheels on an axle |
3.1-2 EOM and first integrals |
3.3-4 Classification of orbits. |
Hwk #4, Ch 3(central forces): 10, 13,
19, 28(a) (due Mon Oct 2, 11:30am) Solutions |
| 5 - Sep 25 - Sep 29 |
3- Central Force Problem | 3.3-4 Classification of orbits: Kepler potential |
3.5,
3.7 Orbit equations, Kepler problem Conic sections: ellipses, hyperbolas |
3.8-9 Eccentric anomaly, LRL vector |
Hwk #5, Ch 3 (Kepler
problem): 11, 21, 23, 24, 33 (due Mon Oct 9, 11:30am) Solutions |
| 6 - Oct 2 - Oct 6 |
3- Central Force Problem | 3.8 Kepler's laws, motion in time, Kepler's equation. |
3.6 Bertrand's theorem, virial theorem. |
Friday: Fall Holiday |
Hwk #6: Ch 3(Scattering):
7, 30, 32, 34, 35 (due Mon Oct 16, 11:30am) Only one problem of (34) and (35) is required, if you solve both, it's for extra credit!. Solutions |
| 7 - Oct 9 - Oct 13 |
3- Central Force Problem, | 3.10-11
(Prof. Luis Lehner) Scattering in a central force field |
Special
lecture: (Prof. Juhan Frank) Three body problem |
3.10-11 (Prof. Jorge Pullin) Scattering in a central force field |
|
| 8 - Oct 16 - Oct 20 |
4- Rigid Body Kinematics | 5.1-2 (Prof. Jorge Pullin) Inertia tensor |
Midterm Review |
4.1-4 Rigid Body Degrees of Freedom, Orthogonal transformations Euler Angles |
Midterm:
Friday Oct 20, 5:30-6:30pm, 118 Nicholson Chapters 1, 2, 3 Midterm Solutions |
| 9 - Oct 23 - Oct 27 |
4, 5- Rigid Body Motion | 4.6,8-9 Euler's theorem Finite and infinitesimal rotations |
4.9-10 Coriolis Force |
5.1-3 Angular momentum, kinetic energy of a rigid body. Inertia tensor, principal axes |
Hwk #7,
Ch 4: 4, 15, 21, 23, 24 (due Wed Nov 1, 11:30am) Solutions |
| 10 - Oct 30 - Nov 3 |
5- Rigid Body Motion | 5.3-5 Inertia tensor, principal axes Euler equations |
5.6-7 Torque free motion Heavy Symmetrical top Earth's wobble: look at the real data |
5.7 Heavy Symmetrical top The stability of the bicycle (D. Jones, Physics Today, Sep'06) |
Hwk #8, Ch 5: 6, 15, 17, 18, 20, 25, 30 (due Fri Nov 10, 11:30am) Solutions |
| 11 - Nov 6 - Nov 10 |
6- Oscillations | 5.8-9 Precession of equinoxes, satellite orbits. |
Damped
Harmonic Oscillator |
Driven
Harmonic Oscillator |
Hwk #9, Ch 6: 4, 8, 11, 12, 15, 18 (due Wed Nov 22, 11:30am) Solutions |
| 12 - Nov 13 - Nov 17 |
6- Oscillations |
Frequencies of free vibration; Normal coordinates |
Linear triatomic molecule. | Triangle triatomic molecule. |
Oleg Korebkin's Mathematica animation of Problem 6-8 (triatomic molecule). |
| 13 - Nov 20 - Nov 24 |
8- Hamilton equations | Canonical equations of motion; Legendre Transformations | Examples | Thanksgiving Holiday |
Hwk #10 (last one!), due Dec 4, 11:30am Ch 8: 2, 7, 13, 16, 20, 22, 23, 26, 35 |
| 14 - Nov 27 - Dec 1 |
8- Hamilton equations 9-Canonical transformations |
A variational principle | Example: 8-22 |
Canonical transformations | |
| 15 - Dec 4 - Dec 8 |
9-Canonical transformations 13- Continuous systems |
Poisson brackets |
Continuous systems A graduate student's work on continuous systems... |
Review |
|
| 16 - Dec 11 - Dec 15 |
Finals week |
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