Symmetries and stability of motions in the Newtonian and the Hookean potentials

Abstract

A new way of looking at symmetries is proposed, especially regarding their role in the stability of two-body motions in the Newtonian and the Hookean potentials, the two selected by Bertrand’s theorem. The role of the number of spatial dimensions is also addressed.

Keywords

• classical mechanics
• dynamical symmetry
• bertrand’s theorem
• kepler problem