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.
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Release date: |
April 2023 |
First published: |
2023 |
Authors: |
Jaume Llibre
• Rafael RamÃrez
• ValentÃn RamÃrez
|
Dimensions: |
235 x 155mm (L x W) |
Pages: |
345 |
Edition: |
1st ed. 2023 |
ISBN-13: |
978-3-03-127094-9 |
Categories: |
Books
|
LSN: |
3-03-127094-0 |
Barcode: |
9783031270949 |
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