An Exactly Conservative Integration Algorithm for the Restricted Three-Body Problem
by
John C. Bowman
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

In the restricted three-body problem of classical mechanics, where one of the bodies has zero mass, traditional integration schemes do not conserve the value of the Jacobi integral. Based on polynomial functions of the time step, such schemes typically lead to systematic drifts in the computed value of this nonlinear first integral of motion. While symplectic integration schemes exactly conserve an approximate Jacobi integral, another class of integration algorithms has recently been developed that conserve the true Jacobi integral to machine precision. These algorithms can be derived simply by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We illustrate the method applied to the restricted three-body problem.

http://www.math.ualberta.ca/~bowman

Date received: February 1, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-88.