School of Physics & Astronomy

# Phys 5011.001

## Classical Physics I

Final Exam
modified 7-Dec-2017 at 11:48AM by Robert Lysak

The final exam for Phys 5011 will be on December 15, 8:30-11:30 am, in Tate 110.

Suggested Problems for Final: Jackson Chapter 4, Problems 7, 9, 13.

 Problem Set 9 (Due Dec. 8) posted 1-Dec-2017 at 11:14AM by Robert Lysak Jackson Chapter 3, Problems 1, 6, 12.

Notes
modified 5-Dec-2017 at 10:04AM by Robert Lysak

In this section, I will post expansions on the notes at various times.

Bessel Functions
modified 5-Dec-2017 at 10:04AM by Robert Lysak

Sturm-Liouville Equations
modified 1-Dec-2017 at 9:54AM by Robert Lysak

modified 1-Dec-2017 at 9:52AM by Robert Lysak

Kepler Problem in Action-Angle Variables
modified 1-Nov-2017 at 11:20AM by Robert Lysak

Motion of Charged Particles in Magnetic and Electric Fields
modified 24-Oct-2017 at 11:31AM by Robert Lysak

Closed Orbits: Bertrand's Theorem
modified 19-Sep-2017 at 2:12PM by Robert Lysak

9/19: These notes give the full derivation of Bertrand's theorem for finite size perturbations. The first page refers to small deviations from circular motion, following section 3.6 of Goldstein and discussed in class. The second page gives the expansion to 3rd order that determines that only the inverse square law and the harmonic oscillator can give closed orbits.

Motivation for the Lagrangian
modified 8-Sep-2017 at 2:08PM by Robert Lysak

9/8: Here is a description of the rather complicated motivation for using the Lagrangian for mechanics. I say "motivation" rather than "derivation" since it is not really a rigorous derivation. However, the proof is in the results: this formulation gives the correct equations of motion in a wide range of circumstances.

Potential Energy for a System of Particles
modified 6-Sep-2017 at 1:18PM by Robert Lysak

9/6: The discussion of potential energy seemed to be confusing. Here is a clearer version of these notes.

 Potential energy for a system of particles | Download posted 6-Sep-2017 at 1:18PM

Problem Set 8 (Due December 1)
modified 6-Dec-2017 at 11:19AM by Robert Lysak

Jackson Chapter 2: Problems 2,5,7.

 No Wednesday Office Hours posted 20-Nov-2017 at 9:55AM by Robert Lysak Due to the Thanksgiving holiday, I will not have office hours on Wednesday, Nov. 22.

Problem Set 7 (Due Nov. 22)
modified 1-Dec-2017 at 11:14AM by Robert Lysak

Jackson Chapter 1: Problems 2,6,7,9.

Quiz 2 (Nov. 9)
modified 13-Nov-2017 at 12:46PM by Robert Lysak

Quiz statistics: Mean 71.6; Median 73; Top Quartile 84; Bottom Quartile 60.

Covers Chapters 6, 8-10, and some parts of Chapter 11 (as in class).

Practice problems: 10.19, 11.1 and 11.5

Hint for 10.19: The integral in r can be done by complex integration in a similar way as in the Kepler problem. In this case, there will be a 3rd order pole, where the residue is lim_u->0 (1/2)(d^2/du^2) (u^3 f(u)).

Problem Set 6 (Due Nov. 3)
modified 9-Nov-2017 at 10:48AM by Robert Lysak

Chapter 10, Problems 8, 13, 18. For problem 10.18, you can assume that the total distance between the walls is d = 3a, i.e., all of the springs are at their unstretched length in equilibrium.

Hint for Problem 10.8: In order to separate the Hamilton-Jacobi equation, try writing the principal function as S = f(t)+x*g(t).

Problem Set 5 (Due Oct. 27)
modified 30-Oct-2017 at 12:07PM by Robert Lysak

Chapter 8, Problems 20, 33; Chapter 9, Problem 22.

Note for problem 8.33, "Investigate the small oscillations..." means find the eigenfrequencies and the relative amplitudes of each body in each mode. For this part, you can assume m1 = m2 = m and 3g / r0 > > 2k / m . You can also assume that the unstretched length of the string is 0.

I have attached a new version of the solution of 8.33 which does not assume the unstretched length is 0 and considers both limits on the ratio of 3g/r0 to 2k/m.

Problem Set 4 (Due October 20)
modified 20-Oct-2017 at 2:01PM by Robert Lysak

Do problems 6.4, 6.12 and the problem in the attached file.

Quiz 1
modified 8-Oct-2017 at 3:43PM by Robert Lysak

Quiz 1 will be on Friday, Oct. 6 in class at 10:10 am in B65. The exam will cover Chapters 1-5 of Goldstein. The exam is closed book, and I will provide a sheet giving important formulas. This sheet will be posted in advance early next week. The following problems from Chapters 4 and 5 will not be graded, but you will be responsible for this material on the quiz:

Chapter 4, Problem 21; Chapter 5, Problems 6, 15, 21.

 Solutions to Quiz 1 Practice Problems | Download posted 2-Oct-2017 at 3:08PM

 TA office hours posted 26-Sep-2017 at 5:20PM by Robert Lysak In my absence, Ragnar Stefansson will have office hours 3:30-5:00 Wednesday in PAN 434.

 Lysak out of town posted 21-Sep-2017 at 10:58AM by Robert Lysak I will be out of town the week of September 25 to attend a conference. During that time we will have guest lecturers: Sept. 25: Rafael Fernandes Sept. 26: Dan Cronin-Hennessey Sept. 27: Joe Kapusta Sept. 29: Tom Jones

Problem Set 3 (Due Sept. 29)
modified 29-Sep-2017 at 1:59PM by Robert Lysak

1. NASA’s Polar satellite is in an orbit around Earth with an apogee of 9.0 RE and a perigee of 1.8 RE, measured from the center of the Earth (1 RE = 1 Earth radius = 6380 km). Determine its semi-major axis, eccentricity and orbital period. Find the energy and angular momentum per unit mass for the satellite. What are its maximum and minimum orbital velocities?

2. Do Problem 3.15

3. Do Problem 3.21

Problem Set 2 (Due Sept. 22)
modified 22-Sep-2017 at 1:59PM by Robert Lysak