Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Time transformation and reversibility of Nambu–Poisson systems

Abstract

Klas MODIN

A time transformation technique for Nambu–Poisson systems is developed, and its structural properties are examined. The approach is based on extension of the phase space P into P¯ = P×R, where the additional variable controls the time-stretching rate. It is shown that time transformation of a system on P can be realised as an extended system on P¯, with an extended Nambu–Poisson structure. In addition, reversible systems are studied in conjunction with the Nambu–Poisson structure. The application in mind is adaptive numerical integration by splitting of Nambu–Poisson Hamiltonians. As an example, a novel integration method for the rigid body problem is presented and analysed.