System for normalization of a hamiltonian function based on lie series

Abstract

A software system for normalization of a Hamiltonian function is described.A few examples of its applications are given. It is written in PASCAL and runs on an IBM XT/AT with 640 KB memory.

Solutions homoclinic to regular precessions of a symmetric satellite

“…An excellent review of the analytical and numerical approximation methods of invariant manifolds can be found in the paper of Sim6 (1990). For these purposes, we used our system LIE Maciejewski, 1990, Maciejewski andGo,4dziewski, 1991) and the normalization was performed up to the sixth order. Properties of the flow on W ~' and W s depend on the type of equilibrium.…”

A First Order Automated Lie Transform

“…Averaging now (10) over [x n−r , x n−r−1 , ..., x 1 ], we get F * * 2 = F 2C * 0,...0 . (6) will give then P 2 = a 1 ,...,a n−r P 2C a 1 ,...,a n−r cos…”

“…After that many authors worked with this theory for example: Sessin [31] shows that the equations generated by the Lie-Deprit's method for unspecified canonical variables could be solved in the same way as Hori [14] did in his method, Ahmed and Tapley [2] shows the equivalence of the generalized Lie-Hori method and the method of averaging. Gozdziewski and Maciejewski [10] gaves a software system for the normalization of a Hamiltonian function based on Lie series.…”