Intermediate Mechanics:Central Force Motion

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Intermediate Mechanics

Second coolest equation ever (T&M 8.21):

$\frac{\partial u}{\partial \dot{\theta}} + u = -\frac{\mu r^2}{l^2}F(r)$

$u = \frac{1}{r}$

Central Force Orbits

$\frac{\alpha}{r} = 1 + \epsilon \cos \theta$

$\epsilon = \sqrt{1 + \frac{2 E L^2}{m K^2}}$

Central Force Motion Orbits

ε value	Orbit Type	Energy Value
ε = 0	Circle
0 < ε < 1	Ellipse	E < 0
ε = 1	Parabola	E = 0
ε > 1	Hyperbola	E > 0