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Non-commuting Variations in Mathematics and Physics:A Survey

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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.

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Detail Information

Series Title

Interaction of Mechanics and Mathematics

Call Number

-

Publisher

Switzerland : Springer Cham., 2016

Collation

XIV, 235

Language

English

ISBN/ISSN

1860-6245

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

1

Subject(s)

Control
Classical Mechanics
Dynamical Systems
Vibration
Mathematical Applications in the Physical Sciences

Specific Detail Info

-

Statement of Responsibility

Serge Preston

Other Information

Cataloger

Devi

Source

-

Validator

Taufik

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