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Do Average Hamiltonians Exist?

Published online by Cambridge University Press:  12 April 2016

S. Ferraz-Mello
S. Ferraz-Mello*
Affiliation:
Instituto Astronômico e Geofísico, Universidade de São Paulo, Caixa Postal 3386, São Paulo, SP, Brasil E-mail: sylvio@usp.br

Abstract

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The word “average” and its variations became popular in the sixties and implicitly carried the idea that “averaging” methods lead to “average” Hamiltonians. However, given the Hamiltonian H = H 0(J) + ϵR(θ,J),(ϵ ≪ 1), the problem of transforming it into a new Hamiltonian H * (J *) (dependent only on the new actions J *), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first.

Information

Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999, pp. 243 - 248
Copyright
Copyright © Kluwer 1999

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