
Dynamics through First-Order Differential Equations in the Configuration Space e-bog
1167,65 DKK
(inkl. moms 1459,56 DKK)
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 fi...
E-bog
1167,65 DKK
Forlag
Birkhauser
Udgivet
25 april 2023
Genrer
Cybernetics and systems theory
Sprog
English
Format
pdf
Beskyttelse
LCP
ISBN
9783031270956
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.