
Ebook: Foundations of Theoretical Mechanics I: The Inverse Problem in Newtonian Mechanics
Author: Ruggero Maria Santilli (auth.)
- Genre: Physics // Mechanics
- Tags: Quantum Physics, Mechanics, Quantum Information Technology Spintronics
- Series: Texts and Monographs in Physics
- Year: 1978
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-14
Elemental Mathematics....Pages 15-53
Variational Approach to Self-Adjointness....Pages 54-109
The Fundamental Analytic Theorems of the Inverse Problem....Pages 110-217
Back Matter....Pages 219-268
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-14
Elemental Mathematics....Pages 15-53
Variational Approach to Self-Adjointness....Pages 54-109
The Fundamental Analytic Theorems of the Inverse Problem....Pages 110-217
Back Matter....Pages 219-268
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