Does a Good Conservation of Jacobi's Constant Imply a Good Orbital Numerical Integration?: I. Resonant Orbits

2003/03/14 by J. Espresate, G. Castro, Espresate, J. +2
Engineering · Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #Space Satellite Systems and Control #astro-ph

paper · pdf · doi:10.48550/arxiv.astro-ph/0303337

27 pages, 2 tables, 11 figures, submitted to Icarus

openalex publication_date 2003/03/14 · arxiv created 2003/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show two examples of numerical orbital integrations (Planar Circular Restricted Three Body Problem) in which even though the conservation of Jacobi's constant is near to 1 part in 10e8, the integration proves to be wrong. That is, for some particular cases the Jacobi's constant is insensitive to very important qualitative (not quantitative) changes in the integrated orbit which are produced by numerical errors. We provide specific recomendations to test and ensure that a numerical code is working properly, regardless the numerical method employed.

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