Jaume Llibre,Rafael Ramirez,Valentin Ramirez
Dynamics through First-Order Differential Equations in the Configuration Space
Dynamics through First-Order Differential Equations in the Configuration Space
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Excellent- More about Dynamics through First-Order Differential Equations in the Configuration Space
This monograph explores the connections between the dynamics of mechanical systems and the Cartesian vector field in the configuration space, presenting new cases of integrability, discussing the Nambu bracket, and offering a solution to the inverse problem in celestial mechanics.
Format: Hardback
Length: 345 pages
Publication date: 26 April 2023
Publisher: Birkhauser Verlag AG
The aim of this monograph is to investigate the feasibility of resolving the dynamics problem within the configuration space rather than the phase space. By introducing a suitable class of vector field, specifically the Cartesian vector field, defined in a Riemann space, the authors delve into the relationships between the first-order ordinary differential equations (ODEs) associated with the Cartesian vector field in the configuration space of a given mechanical system and its corresponding dynamics. The outcome of this exploration yields a novel perspective for studying the dynamics of mechanical systems, enabling the authors to present new instances of integrability for the Suslov and Veselova problem. Furthermore, they establish a connection between the Cartesian vector field and the integrability of the geodesic flow in a specific class of homogeneous surfaces. They also discuss the significance of the Nambu bracket in the study of first-order ODEs and propose a solution for the inverse problem in celestial mechanics.
The aim of this monograph is to investigate the feasibility of resolving the dynamics problem within the configuration space rather than the phase space.
By introducing a suitable class of vector field, specifically the Cartesian vector field, defined in a Riemann space, the authors delve into the relationships between the first-order ordinary differential equations (ODEs) associated with the Cartesian vector field in the configuration space of a given mechanical system and its corresponding dynamics.
The outcome of this exploration yields a novel perspective for studying the dynamics of mechanical systems, enabling the authors to present new instances of integrability for the Suslov and Veselova problem.
Furthermore, they establish a connection between the Cartesian vector field and the integrability of the geodesic flow in a specific class of homogeneous surfaces.
They also discuss the significance of the Nambu bracket in the study of first-order ODEs and propose a solution for the inverse problem in celestial mechanics.
Weight: 717g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031270949
Edition number: 1st ed. 2023
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