PH6246, Section 3916, Fall 2015, Homework 6
Due at the start of class on Monday, October 19.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and sh
PHZ 6607 Fall 2016
Homework #4, Due Friday, October 7
1. Prove the relativistic tensor virial theorem: for an isolated system with finite extent
Z
3
d xT
ij
1 d2
=
2 dt2
Z
d3 x xi xj T 00 .
2. (a) Show that the gradient of the four-velocity u can be decom
PHY6246, Section 3916, Fall 2016, Homework 5
Due at the start of class on Monday, October 3.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and sh
PHY6246, Section 3916, Fall 2016, Homework 7
Due at the start of class on Monday, October 17.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and s
PHY6246, Section 3916, Fall 2016, Homework 6
Due at the start of class on Monday, October 10.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and s
Classical Mechanics
Solution Set 14
Due: 4 December 2013
52. G. Problem 10.14.
Solution: Write out the energy as a curve in phase space:
p2
k
= E < 0,
2m |x|
2mk
+ 2mE
|x|
p=
(1)
The turning points are x = k/|E |. The action variable is
k /|E |
2I =
2mk
+
Classical Mechanics
Solution Set 13
Due: Noon, 2 December 2013
49. We have learned that the Hamiltonian for a charged particle moving in an electromagnetic
eld B = A, E = A involves the potentials
H=
1
(p q A)2 + q .
2m
(1)
However, we have not yet addres
Formulae for Classical Mechanics
Action and Hamiltonian
t2
dtL(qk (t), qk (t), t),
I=
H
t1
Particle of charge Q in EM eld
m
L = r 2 + Q(r A ),
2
qi
i
L
L
qi
E = A
B = A,
Center of mass and relative coordinates (2 bodies)
R=
m1 r 1 + m2 r 2
,
m1 + m2
J
r
Classical Mechanics
Solution Set 1
Due: 28 August 2013
This and all future homework will be posted on the course webpage:
http:/www.phys.u.edu/thorn/homepage/cminfo.html
In the homework assignments, I will refer to problems in Goldstein by prexing the pro
PH6246, Section 3916, Fall 2015, Homework 3
Due at the start of class on Friday, September 25.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and
PH6246, Section 3916, Fall 2015, Homework 4
Due at the start of class on Friday, October 2.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and sho
PH6246, Section 3916, Fall 2015, Homework 10
Due at the start of class on Friday, November 20.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and
I. BEHAVIOUR AND SOLUTIONS OF
ORDINARY DIFFERENTIAL EQUATIONS
Suppose we have a general second order operator
d
d2
+p
+q y =0 .
2
dx
dx
(1.1)
Let us substitute the following
y = e f (x)dx z .
y
z
=f+
y
z
d
One nds (prime denoting dx )
(1.2)
(1.3)
y (n+1)
PH6246, Section 3916, Fall 2015, Homework 9
Due at the start of class on Friday, November 13.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and s
PH6246, Section 3916, Fall 2015, Homework 8
Due at the start of class on Thursday, November 5.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and
PH6246, Section 3916, Fall 2015, Homework 7
Due at the start of class on Friday, October 23.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and sh
PH6246, Section 3916, Fall 2015, Homework 5
Due at the start of class on Friday, October 9.
Answer all questions. Please write neatly and include your name on the front page of your
answers. To gain maximum credit you should explain your reasoning and sho
Midterm, Fall 2011, Graduate Classical Mechanics
1. A particle moves in a quadratic potential in one dimension. It is perturbed by a small, third
order contribution to the potential: V3 = x3 /3.
a) Starting from a Lagrangian, nd the equation of motion for
PHY 6246 Graduate Classical Mechanics
Mid-term Exam
Thursday October 26th, 1995
5:30pm-7:30pm
Read and answer all questions carefully. All questions are of equal weight. Good luck
1
1
Consider the following complete solution to some Hamilton-Jacobi equati
Classical Mechanics
Solution Set 5
Due: 25 September 2013
17. G, Problem 3.27.
Solution: Following the method of problem G, 3.24, we rst write the espression for r
appropriate for hyperbolic motion E > 0 and e > 1:
E=
m2 k
J2
m
k ka(e2 1)
k
=
r +
= r2 +
2
Classical Mechanics
Solution Set 4
Due: 18 September 2013
13. G, Problem 3.18.
Solution: At perigee, the particle velocity and hence its momentum is perpendicular to the
radial direction. The impulse instantaneously changes its momentum by the amount S r
Classical Mechanics
Solution Set 3
Due: 11 September 2013
9. A striking fact about simple harmonic motion is that the period of oscillation is independent of the amplitude of oscillation. This is clearly not true about the oscillations of a
pendulum, thou