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Foundations of Theoretical Mechanics I

The Inverse Problem in Newtonian 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 1-14
  3. Ruggero Maria Santilli
    Pages 15-53
  4. Ruggero Maria Santilli
    Pages 54-109
  5. Ruggero Maria Santilli
    Pages 110-217
  6. Back Matter
    Pages 219-268

About this book

Introduction

The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: I. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 1. The identification of the methods for the construction of a Lagrangian or Hamiltonian from the given equations of motion; and 3. The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.

Keywords

Hamiltonian Hamilton’s principle Newtonian mechanics Potential curvilinear coordinates dynamics elementary particle physics mechanics momentum particle physics relativity solution statistical mechanics theory of relativity thermodynamics

Authors and affiliations

  • Ruggero Maria Santilli
    • 1
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-86757-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1978
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-86759-0
  • Online ISBN 978-3-642-86757-6
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site