Non-commuting Variations in Mathematics and Physics
A Survey
Authors: Preston, Serge
Free Preview- 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
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- About this book
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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.
- Table of contents (9 chapters)
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Basics of the Lagrangian Field Theory
Pages 3-15
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Lagrangian Field Theory with non-commuting variations
Pages 17-49
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Vertical connections, K-twisted prolongations and the NC-variations
Pages 53-78
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Twisted prolongations and the NC-variations
Pages 79-109
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Applications: Holonomic and non-Holonomic Mechanics, H.Kleinert Action principle, Uniform Materials, Non commutative variations and the Dissipative potentials
Pages 111-138
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Table of contents (9 chapters)
- Download Preface 1 PDF (142.7 KB)
- Download Sample pages 2 PDF (466.4 KB)
- Download Table of contents PDF (177.3 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Non-commuting Variations in Mathematics and Physics
- Book Subtitle
- A Survey
- Authors
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- Serge Preston
- Series Title
- Interaction of Mechanics and Mathematics
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-28323-4
- DOI
- 10.1007/978-3-319-28323-4
- Softcover ISBN
- 978-3-319-28321-0
- Series ISSN
- 1860-6245
- Edition Number
- 1
- Number of Pages
- XIV, 235
- Number of Illustrations
- 11 b/w illustrations
- Topics
