Angular Momentum

Two masses (M) rest on a track that rotates around the axis (A). If they are not fixed, centrifugal force will fling them outwards. These masses are synchronously pushed further inwards by an actuator. The speed of the masses causes the system to rotate faster. However, since the actuator must work against the centrifugal force, additional energy is supplied to the system, and it rotates even faster.
Conservation of angular momentum:
To change the speed of a rotating disk, a force must be applied. It's like a lever: at half the radius, twice the force is required.
Planetary motion:
The central acceleration G·M/R² is reduced by the radial acceleration (centrifugal force) of the velocity component perpendicular to the radius (VR)²/R. VR can be calculated using the angular momentum (l). The remaining acceleration is then:

R''= G·M/R²-(l/m)²/R³

Radial acceleration:
In an accelerated system, vertical lines are curved. The distance traveled, s, is calculated as s0+v0·t+(a/2)·t², where a is the constant acceleration. Let s0 = v0 = 0, a = 2·s/t². The curvature of a circle 1/R can be approximated using three points on a parabola.
1/R=(sleft+ sright-2·smiddle)/h², where h is äquidistant, h = VR·t, sleft = sright = 0
Substituting 2·s with -2·smiddle = - h²/R, a = -h²/(R·t²) = -(VR)²/R. The sign changes depending on whether centripetal or centrifugal acceleration is assumed.

Ludwig Resch