Homework 9: # 8.19, 8.24, 8.25
Michael Good
Nov 2, 2004
8.19
The point of suspension of a simple pendulum of length l and mass m is constrained to move on a parabola z = ax2 in the vertical plane. Der
Homework 5: # 3.31, 3.32, 3.7a
Michael Good
Sept 27, 2004
3.7a Show that the angle of recoil of the target particle relative to the incident
1
direction of the scattered particle is simply = 2 ( ).
An
Homework 7: # 4.22, 5.15, 5.21, 5.23, Foucault
pendulum
Michael Good
Oct 9, 2004
4.22
A projectile is red horizontally along Earths surface. Show that to a rst
approximation the angular deviation from
Homework 1: # 1.21, 2.7, 2.12
Michael Good
Sept 3, 2004
1.21. Two mass points of mass m1 and m2 are connected by a string passing
through a hole in a smooth table so that m1 rests on the table surface
Homework 4: # 2.18, 2.21, 3.13, 3.14, 3.20
Michael Good
Sept 20, 2004
2.18 A point mass is constrained to move on a massless hoop of radius a xed
in a vertical plane that rotates about its vertical sy
Homework 12: # 10.13, 10.27, Cylinder
Michael Good
Nov 28, 2004
10.13
A particle moves in periodic motion in one dimension under the inuence of a
potential V (x) = F |x|, where F is a constant. Using
Homework 3: # 2.13, 2.14
Michael Good
Sept 10, 2004
2.13 A heavy particle is placed at the top of a vertical hoop. Calculate the
reaction of the hoop on the particle by means of the Lagranges undeterm
Homework 3: # 2.13, 2.14
Michael Good
Sept 10, 2004
2.13 A heavy particle is placed at the top of a vertical hoop. Calculate the
reaction of the hoop on the particle by means of the Lagranges undeterm
Homework 11: # 10.7 b, 10.17, 10.26
Michael Good
Nov 2, 2004
10.7
A single particle moves in space under a conservative potential. Set up
the Hamilton-Jacobi equation in ellipsoidal coordinates u, v
Homework 8: # 5.4, 5.6, 5.7, 5.26
Michael Good
Oct 21, 2004
5.4
Derive Eulers equations of motion, Eq. (5.39), from the Lagrange equation of
motion, in the form of Eq. (1.53), for the generalized coor
Homework 10: # 9.2, 9.6, 9.16, 9.31
Michael Good
Nov 2, 2004
9.2
Show that the transformation for a system of one degree of freedom,
Q = q cos p sin
P = q sin + p cos
satises the symplectic conditio
Homework 1: # 1, 2, 6, 8, 14, 20
Michael Good
August 22, 2004
1. Show that for a single particle with constant mass the equation of motion
implies the follwing dierential equation for the kinetic ener
General Relativity Exam
Michael Good
April 25, 2006
Problem 3
Taking Robertson-Walker metric
ds2 = dt2 + R(t)2
dr2
+ r 2 d 2
1 kr2
with k = +1, 0, 1 and R(t) the cosmological scale. Use G = 8T and
T ;
Goldstein Chapter 1 Exercises
Michael Good
July 17, 2004
1
Exercises
11. Consider a uniform thin disk that rolls without slipping on a horizontal
plane. A horizontal force is applied to the center of
Goldstein Chapter 1 Derivations
Michael Good
June 27, 2004
1
Derivations
1. Show that for a single particle with constant mass the equation of motion
implies the follwing dierential equation for the k