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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.) In cases where it can be used, it produces a 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 them significantly, and Jacobi integral produces an approximation that depends upon this insignificance. Short-term insignificance may not hold over the long term, e.g., Secular motion, so the Jacobi integral has more use regarding short-term situations.


(mathematics,mechanics)
http://en.wikipedia.org/wiki/Jacobi_integral

Referenced by:
N-Body Problem

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