Solutions to Problems in Goldstein,
Classical Mechanics, Second Edition
Homer Reid
October 29, 2002
Chapter 9
Problem 9.1
One of the attempts at combining the two sets of Hamiltons equations into one
tries to take q and p as forming a complex quantity. Sh
co *$1,
pro/e
erre5b
A pevrC* L^, P .,tole n' G.s ^n r xCLt^\ f)"
L nn ina
A:L
r
l):4.
Rt1cosx)
nnJ
Z.
rnR X
ax =
h = pi  \= cfw_nrd*'l R$
ItJ a*ir r<sisfa.n(l is ^ot

(rGs'<)
V=
R
nnj ( fCosx)
at X:b,
c oo s i ote ,.'eJ , the ene,33
of tt"e t5tl
f<
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l\= r"=L
,pt.
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h" r<
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f o rlserver(.
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,
OF
=O
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Y
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t
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=
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t
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)
rt,*.,f , ' shpcd 4!=f
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T =:]v\U *a
[
rq i s
4. frr.^
drl:rr&'7n+fu'U :
&=
o'
)'n(q*
l'1
:*
So

rn .' s ouvadot l .
I
Y'v\T :
\L
d (,^.T )
att
( l^sq
+
I
att
g
rs2
Yh r)
\s
=te 'PP
=F _
P
:J
(
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P"\J
dT *
Chapter 4.
Lagrangian Dynamics
(Most of the material presented in this chapter is taken from Thornton and Marion, Chap.
7)
4.1 Important Notes on Notation
In this chapter, unless otherwise stated, the following notation conventions will be used:
1. Einste