Author:
Duarte Gladston,Jorba Àngel
Abstract
AbstractIn this paper, we present a way of combining the computation of invariant tori and their stable and unstable manifolds with the multiple shooting technique. We start by showing some of the results of Jorba (Nonlinearity 14(5):943–976, 2001) that should be modified in order to introduce the multiple shooting technique in these computations. After that, by a direct application in the planar elliptic restricted three-body problem (PERTBP), how to modify the equations and methods to compute the above-mentioned objects is introduced. In particular, the structure of the (systems of) equations and matrices involved in these computations is shown. An application of these computations can be found in Duarte and Jorba (Invariant manifolds of tori near $${L}_1$$
L
1
and $${L}_2$$
L
2
in the planar elliptic restricted three-body problem II. The Dynamics of Comet Oterma, Preprint 2023), where the dynamics of comet 39P/Oterma is modelled as a PERTBP.
Funder
Ministerio de Economía y Competitividad
Narodowe Centrum Nauki
Ministerio de Ciencia, Innovación y Universidades
Generalitat de Catalunya
Universitat de Barcelona
Publisher
Springer Science and Business Media LLC
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