Problem #4

Abstract

The problem proposed here is that of performing a Lie transformation.The Lie transform as described by Deprit (1969) is a means of solving certain sets of ordinary differential equations by repeated approximation and he has applied the technique to the problems of predicting the motion of the Moon and also of artificial satellites. Deprit's work contains a remarkable application of symbolic techniques to real problems and it is for this reason that the Lie transform is an interesting calculation.The Lie transform is useful when we have to find a formal solution to a set of ordinary differential equations that have Hamiltonian form, namely dx.BX, 1 BH 1