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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.
| Autorius: | Jaume Llibre, Valentín Ramírez, Rafael Ramírez, |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2024 |
| Knygos puslapių skaičius: | 368 |
| ISBN-10: | 3031270975 |
| ISBN-13: | 9783031270970 |
| Formatas: | 235 x 155 x 20 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Dynamics through First-Order Differential Equations in the Configuration Space“
