Application of Computer in Qualitative Studies of Celestial Mechanics
The ordinary differential equations describing the motion of celestial bodies or other problems and the corresponding mappings are almost all non-integrable, very complicated nonlinear systems. For this reason, even in studying qualitatively some behaviours of simple dynamical models such as instabilities, chaos and asympototic regime we will encounter theoretical difficulties, as V.I. Arnold pointed out: “ The non-integrable problems of dynamics appear inaccessible to the tools of modern mathematics ”. Therefore, it is important to explore the behaviour of the above problems with a computer. In other words, a computer can be a laboratory for qualitative studies in celestial mechanics. This paper will present some examples on the applications of a computer in studies of dynamical systems related to celestial mechanics. It will be divided into two parts.
KeywordsInvariant Manifold Celestial Body Celestial Mechanic Orbital Resonance Theoretical Difficulty
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