Classical Particle in a Coulomb-Like Radial Potential

This Demonstration shows the negative energy trajectories of a point mass moving in the radially symmetric potential U(x,y,z)-(x2+y2+z2)-α/2. Due to the radial symmetry the point mass moves in a two-dimensional plane perpendicular to the angular momentum vector.
The case of corresponds to the Coulomb potential, where negative energy trajectories are periodic. For , all the negative energy trajectories go through the origin.

SNAPSHOTS

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DETAILS

All physical values displayed have been made to be dimensionless.
The initial velocity of the moving point mass is perpendicular to the radius.
Newton's equations of motion in polar coordinates read:
and ,
where is the angular momentum.
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