A potential V(r) = -k/r^4 A very superficial analysis

[yxgao]

What are the general features of this potential? Is the particle attracted or repelled? You don't need to perform a mathematical analysis, but qualitatively, what is the general shape of the orbits? Assume energy is positive. What happens if angular momentum is zero?

[arcnets]

Originally posted by yxgao
Is the particle attracted or repelled?Attracted.what is the general shape of the orbits?Curved toward the center, but not closed (the're only closed for V \sim r^{-1}, Kepler motion). I guess they look like a pattern produced by a spirograph.What happens if angular momentum is zero? The body will fall into the center. From there, it will not be possible to calculate the further motion because of the singularity.