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Dynamics through first-order differe...

Llibre, Jaume.

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Dynamics through first-order differential equations in the configuration space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamics through first-order differential equations in the configuration space/ by Jaume Llibre, Rafael Ramirez, Valentin Ramírez.
Author:	Llibre, Jaume.
other author:	Ramirez, Rafael.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xxii, 345 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Dynamics - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-031-27095-6
ISBN:	9783031270956

Dynamics through first-order differential equations in the configuration space
Llibre, Jaume.

Dynamics through first-order differential equations in the configuration space[electronic resource] /by Jaume Llibre, Rafael Ramirez, Valentin Ramírez. - Cham :Springer Nature Switzerland :2023. - xxii, 345 p. :ill., digital ;24 cm.

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.

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: 9783031270956

Standard No.: 10.1007/978-3-031-27095-6doiSubjects--Topical Terms:

612742
Dynamics
--Mathematics.

LC Class. No.: TA352 / .L55 2023

Dewey Class. No.: 515.39

Dynamics through first-order differential equations in the configuration space
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245 1 0 $a Dynamics through first-order differential equations in the configuration space $h [electronic resource] / $c by Jaume Llibre, Rafael Ramirez, Valentin Ramírez.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2023.
300 $a xxii, 345 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Dynamics $x Mathematics. $3 612742
650 0 $a Configuration space. $3 713541
650 0 $a Differential equations. $3 517952
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Dynamical Systems. $3 3538746
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Mathematical Physics. $3 1542352
700 1 $a Ramirez, Rafael. $3 657663
700 1 $a Ramirez, Valentin. $3 3632387
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773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-27095-6
950 $a Mathematics and Statistics (SpringerNature-11649)