Overview
- A survey of non-commuting Variations in Mathematics and Physics
- Presents and develops methods of analysis, potential classification and of study of dissipative patterns of behavior using classical methods of differential geometry and variational calculus
- Presents a large number of examples of geometrical description of different dynamical behavior in the evolutional systems of partial and ordinary differential equations and characteristics of their irreversible behavior
- Demonstrates that a large variety of irreversible dynamical behavior in physical, mechanical, etc. systems is covered by the Lagrangian formalism with non-commutative variations
- Includes supplementary material: sn.pub/extras
Part of the book series: Interaction of Mechanics and Mathematics (IMM)
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Table of contents (9 chapters)
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Front Matter
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Non-commuting variations - elementary topics
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Front Matter
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Vertical connections and the twisted prolongations
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Front Matter
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APPENDIX . Fibre bundles,jet bundles and the Noether balance laws
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Front Matter
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Back Matter
Keywords
About this book
This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations.
Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.
Authors and Affiliations
Bibliographic Information
Book Title: Non-commuting Variations in Mathematics and Physics
Book Subtitle: A Survey
Authors: Serge Preston
Series Title: Interaction of Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-319-28323-4
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-28321-0Published: 11 March 2016
eBook ISBN: 978-3-319-28323-4Published: 02 March 2016
Series ISSN: 1860-6245
Series E-ISSN: 1860-6253
Edition Number: 1
Number of Pages: XIV, 235
Number of Illustrations: 11 b/w illustrations
Topics: Vibration, Dynamical Systems, Control, Mathematical Applications in the Physical Sciences, Classical Mechanics