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