Homework due on Nov 18th for Classical Mechanics
Fetter-Walecka – Chapter 6 – 15 3 dimensional oscillator
Goldstein Chapter 10 problem 15
A particle of mass m moves in a one dimension subject to the potential
V (x ) =
a
 x
sin 2 
 x0



Obtain an integral expression for Hamilton’s characteristic function. Under what
conditions can action-angle variables be used? Assuming these are met, find the
frequency of oscillation by the action-angle method. (the integral for J can be evaluated
by manipulating the integrand so that the square root appears in the denominator). Check
your results in the limit of oscillations of small amplitude.
30
25
20
15
10
5
0.5
1.0
1.5
2.0
2.5
3.0