# HELP Motion in inverse cubic force field thx 1000000 in advance

1. Oct 2, 2004

### Odyssey

HELP PLZ!! Motion in inverse cubic force field...thx 1000000 in advance!!

Say a particle expereinces a net force F = -Amr^-3, where A is some constant, m is the mass of the particle (point mass), and r is the distance. How should I go about in describing the possible orbits of the particle with non-zero angular momentum and E=0, E<0 and E>0 (ie. describing the shape of its orbit)? I know this would involve some integration and differential equation.

I know that r can be viewed as a function of theta, and the energy E and angular momentum can be written as

E = (1/2) mR'(θ(t))^2θ'(t)^2+(1/2)mR(θ(t))^2θ'(t)^2+V(r(θ(t)))

and

L = mR(θ(t))^2θ(t),

in polar coordinate form

How should I find V(r(θ(t)))? Is it V = integral of F?
How should my answer look like approximately? I have no clue in how my answer will be in terms of what variables.

Any help would be greatly appreciated. Thanks in advance.