Motion in a Central Field

maximal time

force exponent n

-1

force constant α

initialposition
initialvelocity
color by time

This demonstrates a planar trajectory in a central field represented by a potential of the form

V(r)=α

n

r

. Motion in a central field is one of the classical problems of classical mechanics. Many interesting phenomena are exhibited by the motion of a small mass in a central field, like Bertrand's theorem, the fall into the center for strongly singular potentials, ….