Format:
1 Online-Ressource (XXII, 345 p. 5 illus., 2 illus. in color.)
ISBN:
9783031270956
Content:
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.
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.
Additional Edition:
ISBN 9783031270949
Additional Edition:
ISBN 9783031270963
Additional Edition:
ISBN 9783031270970
Additional Edition:
Erscheint auch als Druck-Ausgabe Llibre, Jaume, 1952 - Dynamics through first-order differential equations in the configuration space Cham : Springer, 2023 ISBN 9783031270949
Additional Edition:
ISBN 3031270940
Language:
English
DOI:
10.1007/978-3-031-27095-6
Author information:
Llibre, Jaume 1952-
