The bifurcation of the equilibria of mechanical systems with symmetrical potential (Q2714632)

The authors discuss the bifurcation of equilibrium states of concervative systems whose potential energy is \(V(x,p)\), with \(x\in \mathbb{R}^n\), \(p\in \mathbb{R}^m\) is the vector of physical parameters. It is assumed that the function \(V(x,p)\) can be represented as NEWLINE\[NEWLINE V(x,p) = W(\xi,p), \quad \xi_i = x_i^2,\;i=1,2,\dots,n. NEWLINE\]NEWLINE The authors propose the method of successive determination of the equilibrium states starting with the trivial ones in accordance with their complexity. The problem of relative equilibria of a rigid body in a circular orbit in a central gravitation field is considered as an example.