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Jacobi integral dorostâl-e Jacobi Fr.: intégrale de Jacobi The integral admitted by the equations of a body of infinitesimal
mass moving under the → ^{2} +
y^{·}^{2}
+ z^{·}^{2}) = U - C,
where the dotted coordinates represent velocities,
_{J}U is potential energy, and C the constant of
integration (→ _{J}zero-velocity surface).
The Jacobi integral has been used for two different purposes:
1) to construct surfaces of zero velocity which limit the regions
of space in which the small body, under given initial conditions,
can move, and 2) to derive a criterion
(→ Tisserand's parameter) for re-identification
of a → comet whose orbit has suffered severe perturbations
by a planet. Also known as Jacobi constant.Named after Karl Gustav Jacobi (1804-1851), a German mathematician
who did important work on elliptic functions, partial differential
equations, and mechanics; → |