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Poisson Brackets

• To: mathgroup at yoda.physics.unc.edu
• Subject: Poisson Brackets
• From: david at therch.chem.usu.edu (David Farrelly)
• Date: Sat, 3 Oct 92 08:20:05 -0600

I'm looking for a way to evaluate Poisson brackets symbolically.  For
example the PB of two componetnts of angular momentum J1, j2 is J3

[J1,J2]=J3.

If I have a large expression that contains powers of components of
several angular momenta then it is awkward to do PB by explicitly
taking derivatives because one must then regroup the resulting
expression in coordinates and momenta.  So I want to program in
the algebraic properties of PB, such as [uv,w]=[u,w]v + u[v,w]
as well as the PB relations for angular momentum.  Seems like
it should be possible.

Does anyone know if something like this exists or any ideas
how to do this in Mma?

Thanks

david farrelly
dept. of chemistry
utah state university