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portada Dynamics through First-Order Differential Equations in the Configuration Space
Type
Physical Book
Publisher
Author
Year
2023
Language
English
Pages
368
Format
Paperback
Dimensions
23.4x15.6x1.9 cm
ISBN13
9783031270963

Dynamics through First-Order Differential Equations in the Configuration Space

Jaume Llibre;Rafael Ramírez;Valentín Ramírez (Author) · Birkhäuser · Paperback

Dynamics through First-Order Differential Equations in the Configuration Space - Jaume Llibre;Rafael Ramírez;Valentín Ramírez

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Synopsis "Dynamics through First-Order Differential Equations in the Configuration Space"

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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