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Almost Poisson brackets for nonholon...

Garcia-Naranjo, Luis Constantino.

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Almost Poisson brackets for nonholonomic systems on Lie groups .

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Almost Poisson brackets for nonholonomic systems on Lie groups ./
Author:	Garcia-Naranjo, Luis Constantino.
Description:	265 p.
Notes:	Adviser: Hermann Flaschka.
Contained By:	Dissertation Abstracts International68-03B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3255669

Almost Poisson brackets for nonholonomic systems on Lie groups .
Garcia-Naranjo, Luis Constantino.

Almost Poisson brackets for nonholonomic systems on Lie groups . - 265 p.

Adviser: Hermann Flaschka.

Thesis (Ph.D.)--The University of Arizona, 2007.

Our examples include the Suslov and the Veselova problems of constrained motion of a rigid body, and the Chaplygin sleigh.Subjects--Topical Terms:

515831
Mathematics.

Almost Poisson brackets for nonholonomic systems on Lie groups .
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035 $a (UMI)AAI3255669
035 $a AAI3255669
040 $a UMI $c UMI
100 1 $a Garcia-Naranjo, Luis Constantino. $3 1282216
245 1 0 $a Almost Poisson brackets for nonholonomic systems on Lie groups .
300 $a 265 p.
500 $a Adviser: Hermann Flaschka.
500 $a Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1669.
502 $a Thesis (Ph.D.)--The University of Arizona, 2007.
520 $a Our examples include the Suslov and the Veselova problems of constrained motion of a rigid body, and the Chaplygin sleigh.
520 $a We present a geometric construction of almost Poisson brackets for nonholonomic mechanical systems whose configuration space is a Lie group G. We study the so-called LL and LR systems where the kinetic energy defines a left invariant metric on G and the constraints are invariant with respect to left (respectively right) translation on G.
520 $a For LL systems, the equations on the momentum phase space, T*G , can be left translated onto g *, the dual space of the Lie algebra g . We show that the reduced equations on g * can be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the standard Lie-Poisson bracket onto the constraint space.
520 $a For LR systems we use ideas of semidirect product reduction to transfer the equations on T*G into the dual Lie algebra, s *, of a semidirect product. This provides a natural Lie algebraic setting for the equations of motion commonly found in the literature. We show that these equations can also be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the Lie-Poisson structure on s * onto a constraint submanifold.
520 $a In both cases the constraint functions are Casimirs of the bracket and are satisfied automatically. Our construction is a natural generalization of the classical ideas of Lie-Poisson and semidirect product reduction to the nonholonomic case. It also sets a convenient stage for the study of Hamiltonization of certain nonholonomic systems.
520 $a In addition we study the almost Poisson reduction of the Chaplygin sphere. We show that the bracket given by Borisov and Mamaev in [7] is obtained by reducing a nonstandard almost Poisson bracket that is obtained by projecting a non-canonical bivector onto the constraint submanifold using the Lagrange-D'Alembert principle.
520 $a The examples that we treat show that it is possible to cast the reduced equations of motion of certain nonholonomic systems in Hamiltonian form (in the Poisson formulation) either by multiplication by a conformal factor, by the use of nonstandard brackets or simply by reduction methods.
590 $a School code: 0009.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, General. $3 1018488
690 $a 0405
690 $a 0605
710 2 $a The University of Arizona. $3 1017508
773 0 $t Dissertation Abstracts International $g 68-03B.
790 $a 0009
790 1 0 $a Flaschka, Hermann, $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3255669