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.
- ISBN:
- 9783031270949
- 9783031270949
-
Category:
- Differential calculus & equations
- Format:
- Hardback
- Publication Date:
-
26-04-2023
- Publisher:
- Birkhauser Verlag AG
- Country of origin:
- Switzerland
- Pages:
- 345
- Dimensions (mm):
- 235x155mm
- Weight:
- 0.72kg
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