Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. II. Motion of a System of Particles

Abstract

In Part I of this work, numerical methods were derived for the solution of the equations of motion of a single particle subject to a central force which conserved exactly the energy and momenta. In the present work, the methodology of Part I is extended, in part, to motion of a system of particles, in that the energy and linear momentum are conserved exactly. In addition, the angular momentum will be conserved to one more order of accuracy than in conventional methods. Exact conservation of the total angular momentum results only for the lowest order numerical approximation, which is equivalent to the "discrete mechanics" presented elsewhere.