منابع مشابه
On the generalized Jacobi equation
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to...
متن کاملThe Generalized Jacobi Equation
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation....
متن کاملThe Generalized Jacobi Equation
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation....
متن کاملGalerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
In this paper we study the convergence of the Galerkin approximation method applied to the Generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman ...
متن کاملGalerkin Approximation of the Generalized Hamilton-jacobi Equation
If u is a stabilizing control for a nonlinear system that is aane in the control variable, then the solution to the Generalized Hamilton-Jacobi-Bellman (GHJB) equation associated with u is a Lyapunov function for the system and equals the cost associated with u. If an explicit solution to the GHJB equation can be found then it can be used to construct a feedback control law that improves the pe...
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ژورنال
عنوان ژورنال: General Relativity and Gravitation
سال: 2008
ISSN: 0001-7701,1572-9532
DOI: 10.1007/s10714-007-0589-x