Taking \(H\) as the reference level for gravitational potential energy, show that the total potential energy \(V\) of the system is given by
$$V = m g \left( 2 \lambda r \cos \theta - 2 r \cos ^ { 2 } \theta - \lambda a \right)$$
Find the set of possible values of \(\lambda\) so that there is more than one position of equilibrium.
For the case \(\lambda = \frac { 3 } { 2 }\), determine whether each equilibrium position is stable or unstable.