5. A particle moves under a central attractive force y/º per unit mass, where r, are the

polar coordinates of the particle in its plane of motion. Show that

d²u

do²

+11==

h²

-1

where u=r¹¹, h is the angular momentum about the origin per unit mass of the particle, and y is a

constant. Find the non-trivial equilibrium point in the u, plane and classify it according to its

de

du

linear approximation. What can you say about the stability of the circular orbit under the central

force?