In this paper, a clear Lie-Poisson Hamilton-Jacobi theory is presented. How to construct a Lie-Poisson integrator by generating function methods is also given, which is different from the Ge-Marsden methods . An example on a rigid body has been given to illustrate this point. © 1995.
Li, S. T., & Qin, M. (1995). A note for Lie-Poisson Hamilton-Jacobi equation and Lie-Poisson integrator. Computers and Mathematics with Applications, 30(7), 67–74. https://doi.org/10.1016/0898-1221(95)00126-J