Theoretical and Mathematical Physics

Foundations of Theoretical Mechanics II

Birkhoffian Generalizations of Hamiltonian Mechanics

Authors: Santilli, Ruggero Maria

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About this Textbook

In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre­ sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order.

Table of contents (4 chapters)

  • Introduction

    Santilli, Ruggero Maria

    Pages 1-11

  • Birkhoff’s Equations

    Santilli, Ruggero Maria

    Pages 12-109

  • Transformation Theory of Birkhoff’s Equations

    Santilli, Ruggero Maria

    Pages 110-198

  • Generalization of Galilei’s Relativity

    Santilli, Ruggero Maria

    Pages 199-279

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-86760-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-642-86762-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Theoretical Mechanics II
Book Subtitle
Birkhoffian Generalizations of Hamiltonian Mechanics
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
1983
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-3-642-86760-6
DOI
10.1007/978-3-642-86760-6
Softcover ISBN
978-3-642-86762-0
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XX, 372
Topics