Lagrangian Reduction, the Euler–Poincaré Equations, and Semidirect Products
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چکیده
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. These reduced variational principles are interesting in their own right since they involve constraints on the allowed variations, analogous to ∗Research partially supported by NSF grant DMS 96–33161 and DOE contract DE–FG0395– ER25251 †Research partially supported by NSF Grant DMS-9503273 and DOE contract DE-FG0395ER25245-A000.
منابع مشابه
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There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. Th...
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تاریخ انتشار 1997