Lecture Notes
Lecture 18, Dec 11: Short demos on rigid body and non-linear motions, followed by a review of all materials covered. For notes on the rigid body and non-linear motions, please see here or here.
Lecture 17, Dec 9: Coupled Oscillators (cont.)
Lecture 16, Dec 4: Coupled Oscillators
Lecture 15, Dec 2: Scattering
Correction: $\sin^\psi \rightarrow \sin^2 \psi$ in Eq 15.27 (thanks, AS!).—9:27PM, Dec 08, 2014
Changes: The diagram in page 4 and the paragraph following it are improved.—11:21AM, Dec 01, 2014
Lecture 14, Nov 25: The Kepler problem, Many-body system
Lecture 13, Nov 20: Central force and the Kepler problem
Lecture 12, Nov 18: Gravity
Addition: A new paragraph in page 1.—12:59PM, Nov 19, 2014
Lecture 11, Nov 13: Effective potential, Constraints, Gravity
Addition: Section 11.3.—1:11AM, Nov 18, 2014
Correction: Missing $m$ restored in line 6 of page 3 (thanks KW!).—1:11AM, Nov 18, 2014
Correction: In page 2, item 4: $T_{eff} \rightarrow K_{eff}$.—7:24PM, Nov 14, 2014
Changes: A diagram, added in Section 11.2.1. More discussion, added in Section 11.2.2. Line → surface in Section 11.3.5. Most equations are numbered.—11:49AM, Nov 10, 2014
Lecture 10, Nov 6: Symmetry, Hamiltonian
Correction: Page 8, paragraph 2, line 5: $p + dq \rightarrow q + dq$.—12:23PM, Nov 09, 2014
Addition: Sections 10.4 and 10.5.—2:03PM, Nov 06, 2014
Lecture 9, Oct 30: The Lagrangian way, Symmetry, Conservation
Addition: Page 13, a new paragraph at the end of this page.—2:21PM, Nov 06, 2014
Correction: Page 6, $x$ and $X$ equations had errors (thanks, ZA!). Now corrected. Also, $v_0$ is kept all the way through in the calculation, as it should be, but a comment is added right after the equation of motion.—10:00AM, Nov 06, 2014
Addition: Footnotes 4 and 5. Also, $C$ is specificed explicitly as a non-zero constant (pages 4 and 5).—12:03PM, Nov 05, 2014
Lecture 8, Oct 28: Principle of least action
Addition: Some highlighted words in Section 8.3.—9:13AM, Oct 28, 2014
Correction: Page 4, line 4, the middle term: the incorrect factor $\frac{1}{2}$ is removed (thanks, ZA!).—9:57AM, Oct 27, 2014
Lecture 7, Oct 22: SHO, driven
Change: The last section, improved (I think).—9:53AM, Oct 29, 2014
Addition: A section on qualtiy factor is added at the end (thanks to CK for his nice question during class, which prompted my addition here).—1:41PM, Oct 28, 2014
Correction: Page 10, just above Eq 7.35: period K → period T.—9:09AM, Oct 21, 2014
Lecture 6, Oct 21: SHO, free or damped
Additions: Example 6.3.4 and plots.—5:32PM, Oct 20, 2014
Lecture 5, Oct 16: Conservation theorems, 1D motion
Addition, Correction: Footnotes 4 and 6 are new, and they reflect what we discussed in class. In the last bullet point of page 6, the last sentence was mathematically incorrect (while physically still very meaningful, if qualified a bit), and is removed. In principle, a saddle point can exist in one dimension in a mathematical sense, as we exemplified in class! At the end of the paragraph just after that bullet point “a saddle point” is added.—12:43PM, Oct 16, 2014
Lecture 4, Oct 14: UCM and SHM
Corrections, Addition: Right after Eq 4.14, $\omega$ was missing in $r \equiv A/\omega_c$. Right before Eq 4.15, $t$ was missing in $\sin (\omega_c t + \theta_0)$. Both corrected (thanks ZA!). Also, footnote 4 added.—6:21PM, Oct 18, 2014
Correction: Four lines below 4.12, at the end: $\ddot x$ → $\ddot y$. (Thanks, ZA!)—9:05AM, Oct 14, 2014
Lecture 3, Oct 9: Air resistance, Non-linear oscillator
Addition: Footnote 6.—8:46PM, Oct 30, 2014
Correction, Addition: Page 11, line 3: $\alpha \rightarrow O(\alpha)$ (thanks NR!). Footnotes 6 and 7 are added.—4:12PM, Oct 21, 2014
Addition: Eq. 3.6 is actually integrable, rather easily by hand, and the result is now added (Eq. 3.9).—9:41PM, Oct 09, 2014
Correction: Eqs. 3.25 (and Eq. 3.27) missed $t_a$ in the middle term. Now, this is fixed, thanks to KD (!), whose question led to this correction. Equation numbers in page 9 are cleaned up as well.—7:27AM, Oct 09, 2014
Lecture 2, Oct 7: Newton’s laws, air resistance
Change: The end of page 4: references to sections and examples are removed.—12:15PM, Oct 07, 2014
Correction: Page 3: Marge box, near the end: last year → 2010.—9:32AM, Oct 07, 2014
Change: The end of page 2: “the textbook” → “various books.”—6:38PM, Oct 06, 2014
Lecture 1, Oct 2: Intro: particles, dimensions, vectors, scalars, matrices…
Addition: A new footnote (1) regarding real and complex numbers.—12:31PM, Oct 17, 2014
Addition, change: A new footnote (3). $L \rightarrow O$ in line 2 of page 7.—12:52PM, Oct 02, 2014
Correction: Pages 6,7, in definition boxes of vector, scalar: linear → orthogonal.—9:38AM, Oct 02, 2014
Appendices
Correction At the end, the case when $v_0$ is non-zero was discussed incorrectly in the Oct 3 version. Now, corrected.—9:25AM, Oct 05, 2014
Addition: Page 8, more physics discussion added at the end.—10:28AM, Oct 03, 2014
Correction, addition: Page 7, the last term in the third order solution had a wrong sign—now corrected. Page 8, discussion added about the exact solution.—9:30PM, Oct 02, 2014
Change: page 6, the first sentence and the equations of the example (A.2) were arranged in a slightly different way.—12:42PM, Oct 02, 2014
Addition: The last section.—7:40PM, Dec 03, 2014