Table of contents
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.
- DOI https://doi.org/10.1007/978-3-319-28323-4
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Springer, Cham
- eBook Packages Engineering Engineering (R0)
- Print ISBN 978-3-319-28321-0
- Online ISBN 978-3-319-28323-4
- Series Print ISSN 1860-6245
- Series Online ISSN 1860-6253
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