§ 1. Ordinary and singular periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton's form where ( q 1 q 2 ) are the generalised co-ordinates, ( p 1 , p 2 ) are the generalised momenta, and where H is a function of ( q 1 , q 2 , p 1 , p 2… Expand