Motion under different kinds of force

 


 

 


Bertrand's theorem:

In central force motion, the orbits are closed only for inverse square law and Hooke's law

Reference

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980), 2nd ed.

Lowell S. Brown Am. J. Phys. 46, 930 (1978)

Y. Tikochinsky, Am. J. Phys. 56, 1073 (1988)