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4.3 Drehimpuls in Polarkoordinaten

PIC

Die Bahn liegt in der x-Ebene, somit ist L parallel zur z-Achse.

Lz = m .(x.vy- y .vx)

x = r.cosf ==> x˙= ˙rcosf + r(- sin f) ˙f

y = r.sin f ==> ˙y = ˙rsin f+ r(cosf) ˙f

x .vy = r˙rsinf cos f+ r2cos2f .˙f

- y.vx = - r˙rsin fcosf + r2sin2f .˙f

( 2 2 2 2 ) 2 ( 2 2 ) 2 Lz = m. r˙rsin fcosf + r cos f.f˙- r˙rsin fcosf + r sin f .˙f = m.rf cos f+ sin f = m.r (t).f˙(t)

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