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Final Exam

modified 7Dec2017 at 11:48AM by Robert Lysak  

The final exam for Phys 5011 will be on December 15, 8:3011:30 am, in Tate 110. Suggested Problems for Final: Jackson Chapter 4, Problems 7, 9, 13.

Problem Set 9 (Due Dec. 8)

posted 1Dec2017 at 11:14AM by Robert Lysak 

Jackson Chapter 3, Problems 1, 6, 12. 
Notes

modified 5Dec2017 at 10:04AM by Robert Lysak  

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

Problem Set 8 (Due December 1)

modified 6Dec2017 at 11:19AM by Robert Lysak  

Jackson Chapter 2: Problems 2,5,7.

No Wednesday Office Hours

posted 20Nov2017 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 1Dec2017 at 11:14AM by Robert Lysak  

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

Quiz 2 (Nov. 9)

modified 13Nov2017 at 12:46PM by Robert Lysak  

Quiz statistics: Mean 71.6; Median 73; Top Quartile 84; Bottom Quartile 60. Covers Chapters 6, 810, 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 9Nov2017 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 HamiltonJacobi equation, try writing the principal function as S = f(t)+x*g(t).

Problem Set 5 (Due Oct. 27)

modified 30Oct2017 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 m_{1} = m_{2} = m and 3g / r_{0} > > 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 20Oct2017 at 2:01PM by Robert Lysak  

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

Quiz 1

modified 8Oct2017 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 15 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.

TA office hours

posted 26Sep2017 at 5:20PM by Robert Lysak 

In my absence, Ragnar Stefansson will have office hours 3:305:00 Wednesday in PAN 434. 
Lysak out of town

posted 21Sep2017 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 
Problem Set 3 (Due Sept. 29)

modified 29Sep2017 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 semimajor 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 22Sep2017 at 1:59PM by Robert Lysak  


Problem Set 1 (Due Sept. 15)

modified 18Sep2017 at 1:54PM by Robert Lysak  

Goldstein Chapter 1, Problems 5, 21, and the following problem: PS1 Problem 3: Consider the double pendulum of Figure 1.4, with each body of mass m and each rod having length L. This system is placed in an external, constant gravitational force. Write down the kinetic and potential energy of the system in terms of the angles and their derivatives and determine the Lagrangian. Find the Lagrangian equations of motion for this system.

Lectures

modified 1Dec2017 at 11:13AM by Robert Lysak 

Sections refer to Goldstein 9/12: Hamilton’s principle; calculus of variations 2.13 9/19: Closed orbits; Kepler problem; Virial Theorm 3.4, 67 9/25: Orthogonal Transformations; Euler angles 4.36 10/2: Lagrangian formulation of Rigid Body Motion 5.7 10/9: Systems of oscillators 6.12 10/16: Conservation Laws; Poisson Brackets; Phase Space 8.2, 9.5 10/23: Angular momentum; HamiltonJacobi theory 9.7, 10.13 10/30: Guiding Center Drifts; Adiabatic Invariants 12.2,5 11/6: Fixed points; Limit Cycles; Strange Attractors 11.34 From here on, section numbers refer to Jackson, except for numbers preceded by LL which are from Landau and Lifschitz, Electrodynamics of Continuous Media. 11/13: Fundamentals of E&M, Gauss and Coulomb’s Laws 1.14 11/20: Numerical Methods; Method of Images 1.1213; 2.1 11/27: Fourier series; Spherical Coordinates 2.93.1 12/4: Cylindrical Coordinates; Bessel functions 3.78 