Physics
6010 home
Note:
these assignments are provisional and subject to
change!
Homework
problems
Assignment 1: Chapter 1 - 8, 9, 10,
14, 18, 19, 20, 21. Due: 9/21
Assignment 2: Chapter 2 - 3-5, 12,
13, 16-19, 22. Due: 10/10
Additional Problem (see
Symmetries and Conservation
Laws: Noether's Theorem):
Consider a system of
Newtonian particles interacting pairwise by central forces. Show
that this system admits a boost symmetry. Use Noether's theorem
to compute the corresponding conserved quantities. What is their
physical interpretation?
Assignment 3:
Chapter 3 - 10, 11,
13, 19, 20,
22, 33 Due: 10/28
Additional Problem (see
First integrals. Reduction. The 2-body
problem.):
Show that the conserved angular momentum of
the relative motion is the total angular momentum of the 2-body system
defined relative to the center of mass.
Assignment 4: Chapter 6 - 1, 3, 12, 14, 16, 18. Due: 11/11
Additional
Problem:
Consider an oscillator, initially at rest, which undergoes a
constant force for a finite period of time. Show that
after the force ceases the system is oscillating harmonically.
Determine the amplitude of the resulting oscillation.
See Forced Oscillations
for details.
Assignment 5:
Chapter 8
- 1a, 2, 15, 16,
19, 23, 26, 35
Chapter 9 - 5, 25, 28a, 30, 31
Extra Credit
Problem:
What is the infinitesimal symmetry responsible for the conservation of
the Laplace-Runge-Lenz vector?