Non-commuting variations in mathematics and physics [electronic resource] : a survey / Serge Preston.
Preston, Serge, author.
2016
QA315
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Title
Non-commuting variations in mathematics and physics [electronic resource] : a survey / Serge Preston.
Author
Preston, Serge, author.
ISBN
9783319283234 (electronic book)
3319283235 (electronic book)
9783319283210
DOI
https://doi.org/10.1007/978-3-319-28323-4
Published
Cham : Springer, 2016.
Language
English
Description
1 online resource (xiv, 235 pages) : illustrations.
Item Number
10.1007/978-3-319-28323-4 doi
Call Number
QA315
Dewey Decimal Classification
515/.64
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed March 8, 2016).
Series
Interaction of mechanics and mathematics series.
Available in Other Form
Print version: 9783319283210
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All Resources
Basics of the Lagrangian Field Theory
Lagrangian Field Theory with the Non-commuting (NC) Variations
Vertical Connections in the Congurational Bundle and the NCvariations
K-twisted Prolongations and -symmetries (by Works of Muriel,Romero
Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials
Material Time, NC-variations and the Material Aging
Fiber Bundles and Their Geometrical Structures, Absolute Parallelism
Jet Bundles, Contact Structures and Connections on Jet Bundles
Lie Groups Actions on the Jet Bundles and the Systems of Differential Equations.

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