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Foundations of Theoretical Mechanics II

Birkhoffian Generalizations of Hamiltonian Mechanics

  • Ruggero Maria Santilli

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Ruggero Maria Santilli
    Pages 1-11
  3. Ruggero Maria Santilli
    Pages 12-109
  4. Ruggero Maria Santilli
    Pages 110-198
  5. Ruggero Maria Santilli
    Pages 199-279
  6. Back Matter
    Pages 281-371

About this book

Introduction

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.

Keywords

Hamiltonian Inverses Problem Mechanik Newtonian mechanics Potential algebra conservation law differential geometry geometry mechanics quantum mechanics relativity space-time statistical mechanics theory of relativity

Authors and affiliations

  • Ruggero Maria Santilli
    • 1
  1. 1.The Institute for Basic ResearchCambridgeDeutschland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-86760-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1983
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-86762-0
  • Online ISBN 978-3-642-86760-6
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site