Theoretical and Mathematical Physics

Foundations of Theoretical Mechanics I

The Inverse Problem in Newtonian Mechanics

Authors: Santilli, Ruggero Maria

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About this Textbook

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.

Table of contents (4 chapters)

  • Introduction

    Santilli, Ruggero Maria

    Pages 1-14

  • Elemental Mathematics

    Santilli, Ruggero Maria

    Pages 15-53

  • Variational Approach to Self-Adjointness

    Santilli, Ruggero Maria

    Pages 54-109

  • The Fundamental Analytic Theorems of the Inverse Problem

    Santilli, Ruggero Maria

    Pages 110-217

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-86757-6
  • 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 978-3-642-86759-0
  • 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 I
Book Subtitle
The Inverse Problem in Newtonian Mechanics
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
1978
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-3-642-86757-6
DOI
10.1007/978-3-642-86757-6
Softcover ISBN
978-3-642-86759-0
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XX, 268
Topics