Lecture notes

• Lecture 16, Nov. 17: Coupled oscillators.

  • Some footnotes and several sentences added. — Sam, 11:15AM, Nov 18, 2011

• Lecture 15, Nov. 15: Collisions, impact parameter, crossection.

  • 'Typically but not always,' added in page 7 (red).

• Lecture 14, Nov. 10: Kepler problem and many particle system.

• Lecture 13, Nov. 8: Kepler problem. (Qs)

  • Correction: page 2, $L_{M} \rightarrow L_{cm}$.

• Lecture 12, Nov. 3: Gravity. (Qs)

• Lecture 11, Nov. 1: Lagrangian with constraint, Effective potential, Gravity.

• Lecture 10, Oct. 25: Hamiltonian. Lagrangian with constraint. (Qs)

• Lecture 9, Oct. 20: Symmetry and conservation. Momentum and angular momentum. (Qs)

• Lecture 8, Oct. 18: Principle of least action. (Green’s function method – solutions)

  • Page numbers corrected. — Sam, 2:25PM, Oct 25, 2011

• Lecture 7, Oct. 13: Driven oscillations. (Qs)

• Lecture 6, Oct. 11: Small oscillations, free or damped. (Qs)

• Lecture 5, Oct. 6: Conservation principles and 1D motions.

• Lecture 4, Oct. 4: Lorentz force. (Qs)

  • Read footnote 3, to clear up the confusion for the number of integration constants.

  • When we consider the time-reversal symmetry of this problem, we do not reverse the direction of $\vec{B}$, taking it as given. If we can reverse the direction of $\vec{B}$ as well as the direction of the particle's motion, then the time reversal symmetry would be valid. Read end of page 4, to see why sometimes $\vec{B}$ is not reversible.

• Lecture 3, Sep. 29: Perturbation. Air resistance. (Qs)

  • Correction: Page 8, a new box on perturbation expansion. 2/3 → 1/3 in 3 lines above the box. — Sam, 1:04PM, Oct 04, 2011

• Lecture 2, Sep. 27: Newton's laws. Air resistance. (Qs)

• Lecture 1, Sep. 22: What to learn? Particles, dimensions. Vectors and (orthogonal) matrices.

Appendices

• A1: Perturbation.

  • Page 5 and examples are important.

• A2: Essential trig identities.