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Physics 325
Spring 2011
Discussion 6
February 28, 2011
A particle of mass
μ
and initial angular momentum
‘
is moving in a central force ﬁeld
F
(
r
) =
kr,
with
k >
0
. Starting from the central force equation
u
00
+
u
=

μ
‘
2
u
2
F
±
1
u
²
,
where
u
0
=
du/dθ
and
u
= 1
/r
, we want to solve for the particle’s path using the following
steps.
(a) If
u
0
= 0
at
u
= 1
/s
, solve for
(
u
0
)
2
as a function of
u
. Here,
s
is given by
s
=
±
‘
2
μk
²
1
/
4
(b) Assuming
u
0
≥
0
, integrate once more to solve for
u
as a function of
θ
. Use initial
condition
r
2
sin
α
=
s
2
at
θ
= 0
, for a given
α
.
Hint:
Make the substitution
u
2
=
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 Physics, mechanics, Angular Momentum, Force, Mass, Momentum

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