Dynamics through first-order differential equations in configuration space [electronic resource] / Jaume Llibre, Rafael Ramírez, Valentín Ramírez.

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Dynamics through first-order differential equations in configuration space [electronic resource] / Jaume Llibre, Rafael Ramírez, Valentín Ramírez.

9783031270956 (electronic bk.)
3031270959 (electronic bk.)
3031270940
9783031270949

Cham : Birkhäuser, 2023.

English

1 online resource

10.1007/978-3-031-27095-6 doi

TA352

515/.39

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed May 8, 2023).

Print version: 9783031270949

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