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Jacobi integral

(method of solving some three-body problems)

The Jacobi integral is a mathematical device useful for analysis and solution of some three-body problems. Three-body problems, like other N-body problems, have no general solution. Essentially the Jacobi integral is a formula of incorporating various parameters of the system with some variants for particular cases. In cases where it can be used, it produces an associated constant, i.e., a conserved quantity, sometimes called its Jacobi constant. The three-body problems for which it can be used are restricted circular three-body problems, problems in which two of the bodies are in a circular orbit and the third body has a mass too small to affect the other two significantly, and Jacobi integral produces an approximation that depends upon this insignificance. Short-term insignificance may not hold over the long term (i.e., secular motion) so the Jacobi integral has more use regarding short-term situations.


(mathematics,mechanics)
Further reading:
https://en.wikipedia.org/wiki/Jacobi_integral
https://scienceworld.wolfram.com/physics/JacobiIntegral.html
https://farside.ph.utexas.edu/teaching/336k/Newton/node121.html
https://gemelli.spacescience.org/~hahnjm/ast_608/2006spring/3body.pdf
https://ui.adsabs.harvard.edu/abs/1961MNRAS.123....1O/abstract

Referenced by page:
N-body problem

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