Notes on Hori Method for Non-Canonical Systems

Author: Fernandes S.d.S.

Source: Celestial Mechanics and Dynamical Astronomy, Volume 87, Number 3, November 2003 , pp. 307-315(9)

Publisher: Springer

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Abstract:

In this paper the new approach for the integration theory of the canonical version of Hori method recently proposed is extended to the non-canonical one. It will be shown that the non-homogeneous ordinary differential equation with an auxiliary parameter t* associated with the mth order equation of the algorithm can also be replaced by a non-homogeneous partial differential equation in the time t. Using a generalized canonical approach, the general algorithm proposed by Sessin is then revised; as well as the Lagrange variational equations for the non-canonical version of Hori method. A simplified algorithm derived from Sessin’s algorithm is presented for non-linear oscillations problem.

Keywords: Hori method; non-canonical systems; integration theory

Document Type: Research article

Affiliations: 1: Departamento de Matemática, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP, Brazil, Email: sandro@ief.ita.cta.br

Publication date: 2003-11-01