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＜電子ブック＞
Dynamics through First-Order Differential Equations in the Configuration Space / by Jaume Llibre, Rafael Ramírez, Valentín Ramírez

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2023
本文言語	英語
大きさ	XXII, 345 p. 5 illus., 2 illus. in color : online resource
著者標目	*Llibre, Jaume author Ramírez, Rafael author Ramírez, Valentín author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Dynamical systems LCSH:Geometry, Differential LCSH:Mathematical physics FREE:Differential Equations FREE:Dynamical Systems FREE:Differential Geometry FREE:Mathematical Physics
一般注記	Chapter. 1. Dynamics via the first order ordinary differential equations -- Chapter. 2. Constrained Cartesian vector fields -- Chapter. 3. Three dimensional constrained Cartesian vector fields -- Chapter. 4. Cartesian-Synge-Cinsov vector field -- Chapter. 5. Generalized Cartesian-Nambu vector fields -- Chapter. 6. Integrability of generalized Cartesian-Nambu vector fields 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 HTTP:URL=https://doi.org/10.1007/978-3-031-27095-6

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