Abstract
These lectures discuss the persistently inherent instability dominating the dynamical behavior of three gravitationally interacting point masses. The masses of the participating bodies are of the same order of magnitude and their mutual distances are arbitrary.
The lectures are organized in the classical inverted style: first all results are presented, then the definitions and the equations of motion in various systems are described. This is followed by the development of the mathematical apparatus needed, the Lagrange-Jacobi equation, Sundman’s original and modified inequalities and several dynamical escape conditions. The principal theorem regarding the stability of the system is then proved with first offering the outline, then an approximation and finally, all the details of the precise derivations. Implications of the results to questions of numerical analysis regarding the accuracy of the numerical integration of three and many-body problems are included.
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Szebehely, V. (1973). Recent Advances in the Problem of Three Bodies. In: Tapley, B.D., Szebehely, V. (eds) Recent Advances in Dynamical Astronomy. Astrophysics and Space Science Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2611-6_9
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DOI: https://doi.org/10.1007/978-94-010-2611-6_9
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