Higher order normal modes (Q2220265)

The authors study Hamiltonian systems with Hamiltonian given by the sum of a classical kinetic energy term (a quadratic function of the momentum) and a potential energy term which is a homogeneous function of the position. Solutions to the equation of motion are found. They are in the form of normal modes, namely the position vector remains on a fixed line passing through the origin. The example of a potential energy which is homogenous of order four is studied in detail.