UID:
almahu_9949482358402882
Format:
XXII, 345 p. 5 illus., 2 illus. in color.
,
online resource.
Edition:
1st ed. 2023.
ISBN:
9783031270956
Content:
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.
Note:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783031270949
Additional Edition:
Printed edition: ISBN 9783031270963
Additional Edition:
Printed edition: ISBN 9783031270970
Language:
English
DOI:
10.1007/978-3-031-27095-6
URL:
https://doi.org/10.1007/978-3-031-27095-6
