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Unformatted text preview: m is conserved in this system, L ≡ mr2 φ, so the
equation of motion for generalized coordinate r can be rewritten as
mr 1 +
R 2 cos2 r
R = L2
R 2 r2 sin
R (b) Are there stationary horizontal circular orbits? This problem can
be solved using the equation of motion or the eﬀective potential, Ueﬀ =
U + L2 /(2mr2 ). A stationary point, r0 is deﬁned by,
∂r = 0.
r=r0 For the eﬀective potential at hand
= − 3 + mg cos
which leads to the transcendental equation
= r0 cos(˜0 ),
m2 R2 gα
where r0 = r0 /R. Dependi...
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