Simulation of the collision of a pair of running kinks on a cosmic string, modeled with the relativistic area-action. Whereas the kinks move with the speed of light (shown here in slow-motion), the transverse velocity of the string is sub-light-speed. These kinks, however, have sufficient amplitude that there are two instants (in the frame of the animation) where one point of the string — the sharp cusp — is moving at exactly the speed of light. In the animation below, the amplitude of one of the kinks is reversed. Now there is a singularity at a single instant of time, simultaneously at two points along the string.

Although in both collisions the kinks are unchanged after the collision, the non-linearity of the collision process is in evidence in the delay of the outgoing kinks. The relativistic string is one of the simplest systems that has spontaneous singularity formation. Violent collision (and reconnection) events on cosmic strings are candidate sources of strong gravitational waves.

### Announcements

- (1/25) A student at the back of the room asked if we would address specific items in the lecture notes that were confusing. Indeed we will, and you can help us (Veit, Jane, Sam) by emailing your questions on the lecture notes in advance (email addresses below).
- (1/25) The office hour sign-up sheet turned out to be useless, because the (random) sample times were interpreted as the only choices! Please email me a set of times that work for you.
- (1/26) Please post lecture note questions on Piazza, instead of using email.
- (1/30) If you are unable to enroll in the course because the discussion section conflicts with another class by 10 minutes, see Rosemary Barber (M-F, 7AM-12, 1PM-3) in 121 Clark.
- (2/11) Please visit our Piazza site to cast your vote for new study hall times.
- (2/11) Because of February Break you have a shorter homework assignment this week and it is due
**Friday**. - (2/14) Alert student Kenneth Vetter spotted a typo in the instructor's
*Mathematica*notebook, with the result that the correct time for one period in problem 1 of Assignment 3 is*T*= 7.2. - (2/21) The second problem in assignment 4 was slightly changed. Be sure to solve today's version.
- (2/24) In response to the poor class performance on one of the problems in assignment 3, an additional problem has been added to assignment 4.
- (3/4) Here is the distribution of scores on the first prelim. Sam will be handing back exams on Tuesday and will go over the problems.
- (3/9) An error in homework assignment 6 was corrected.
- (3/9) Because of the cleanup work in Clark 294D, the discussion next week will be held in Clark 220.
- (3/15) It's a snow day! On Friday we will discuss lectures 19 and 20 and have two 2-minute-TAs.
- (3/16) The discussion section will meet in Clark 220 at least until Spring Break.
- (3/21) Veit Elser regrets that he is not able to have office hours today. As compensation, he will have office hours 2:00-4:00 on Wednesday and Thursday.
- (3/24)
**By popular demand, the second prelim has been moved to Wednesday, April 12.** - (4/18) Here is the distribution of scores on the second prelim.
- (4/27) Homework assignment 12 was reposted with a hint for the third problem.
- (5/18) Here is the distribution of scores on the final.
- (5/22) Graded finals may be picked up starting today in 426 PSB.

### Course Information

- prerequisites: freshman physics, multivariable calculus, linear algebra, differential equations
- two in-class prelims, final exam
- one homework assignment almost every week
- grade: homework 35%, prelims 20% (each), final 25%
- no text, all lectures available for download

### Syllabus

- rigid body motion and fictitious forces
- generalized coordinates and the Lagrangian formalism
- constrained motion
- symmetry and conservation laws
- calculus of variations
- action principles
- classical mechanics as an approximation of quantum mechanics
- phase space and the Hamiltonian formalism
- canonical transformations
- adiabatic invariance
- gravitational two-body problem
- geometric action principles and special relativity

### Lectures

- lecture attendance is required
- "lectures" are review sessions of the online lecture material (below)
- your participation will be noted
- it is essential you read the lecture material
**before the date of the review** - occasionally the lecturer will do a derivation, so you see first-hand how it's done
- do not plan on taking lecture notes but bring paper and pen for short calculations
- no open laptops during lecture

- January 27
- January 30
- February 1
- February 3
- February 6
- February 8
- February 10
- February 13
- February 15
- February 17
- February 22
- February 24
- February 27
- March 3
- March 6
- March 8
- March 10
- March 13
- March 15
- March 17
- March 20
- March 22
- March 24
- March 27
- March 29
- March 31
- April 10
- April 14
- April 17
- April 19
- April 21
- April 24
- April 26
- April 28
- May 1
- May 3
- May 5
- May 8
- May 10

### Homework (given date is the due date)

- February 3 solution
- February 13 solution
- February 17 solution
- February 27 solution
- March 6 solution
- March 13 solution
- March 20 solution
- March 27 solution
- March 31 solution
- April 17 solution
- April 24 solution
- May 1 solution
- May 10 solution

### Study Group

- informal space to work on homework with other 3318 students
- 294C Clark, Thursday & Friday 4-6 PM

### Exams

- prelim 1: Wednesday, March 1 (in class)
- prelim 2: Wednesday, April 12 (in class)
- final:
**Monday, May 15, 9-11:30 AM, 132 Rockefeller**

### Staff Information

- lecturer: Veit Elser, email, office: 426 PSB, office hours: Tuesdays 3:30-4:30 PM
- co-lecturer: Jane Wang, email, office: 517 Clark, office hours: Monday 3:00-4:00 PM
- TA: Sam Kachuck, email, office: 2149 Snee Hall, office hours: Wednesday 4:30-6:00 PM
- grader: Ti-Yen Lan, email, office: 425A PSB
- Undergraduate TA: Robert Delgado, email

### Software

- orbits on the rotational energy ellipsoid (
*Mathematica*) - phase space mixing in Yang-Mills dynamics (
*Mathematica*)