Jacobi integral

In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem.^[1] Unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases.

It was named after German mathematician Carl Gustav Jacob Jacobi.

^ Bibliothèque nationale de France. Jacobi, Carl G. J. (1836). "Sur le movement d'un point et sur un cas particulier du problème des trois corps". Comptes Rendus de l'Académie des Sciences de Paris. 3: 59–61.

[BnF-1] Bibliothèque nationale de France. Jacobi, Carl G. J. (1836). "Sur le movement d'un point et sur un cas particulier du problème des trois corps". Comptes Rendus de l'Académie des Sciences de Paris. 3: 59–61.

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