Dynamics through First-Order Differential Equations in the Configuration Space
Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín
ISBN 10: 3031270967 ISBN 13: 9783031270963
Published by Birkhäuser, 2023
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Ria Christie Collections, Uxbridge, United Kingdom
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The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field - the Cartesian vector field - given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
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Title: Dynamics through First-Order Differential ...
Publisher: Birkhäuser
Publication Date: 2023
Binding: Soft cover
Condition: New
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