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.
In celestial mechanics, Jacobi'sintegral (also known as the Jacobiintegral or Jacobi constant) is the only known conserved quantity for the circular...
example inverting elliptic integrals and focusing on the nature of elliptic and theta functions. In his 1835 paper, Jacobi proved the following basic...
field Jacobi's four-square theorem Jacobi form Jacobi's formula Jacobi group Jacobian ideal Jacobi identity JacobiintegralJacobi's logarithm Jacobi method...
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Sir Derek George Jacobi CBE (/ˈdʒækəbi/; born 22 October 1938) is an English actor. Jacobi is known for his work at the Royal National Theatre and for...
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In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P n α...
zero-velocity surface in space which cannot be passed, the contour of the Jacobiintegral.[not verified in body] When the object's energy is low, the zero-velocity...
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In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration...
Carl Gustav Jacobi. Abel discovered elliptic functions by taking the inverse function φ {\displaystyle \varphi } of the elliptic integral function α (...
as the most general 2 quasi-period function. The Jacobi theta functions have the following integral representations: ϑ 00 ( z ; τ ) = − i ∫ i − ∞ i +...
constant as the object resides at the initial position. It is the first time-integral of the displacement (i.e. absement is the area under a displacement vs...
modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi in 1826. The most common domain of integration for such a rule is taken...
shown mathematically to be conserved throughout the motion. The Hamilton–Jacobi equations provide a commonly used and straightforward method for identifying...
In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky for one of three finite sequences of orthogonal polynomials y. Since they form...
Abel function Abel's integral equation Abel's identity Abel's inequality Abel's irreducibility theorem Abel–Jacobi map Abel–Jacobi theorem Abel polynomials...
topology. In this formulation, the solutions of the Hamilton–Jacobi equations are the integral curves of Hamiltonian vector fields. Routhian mechanics is...
Abelian integrals, which become the well known elliptic integrals if 2 axes are set equal. Königsberg, 28th Dec. '38. The solution given by Jacobi (Jacobi 1839)...
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