Foundations of Theoretical Mechanics I The Inverse Problem in Newtonian Mechanics
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1978, 1978
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| Edition: | 2nd ed. 1978 |
| Series: | Texts and Monographs in Physics
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| Subjects: | |
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Elemental Mathematics
- 2 Variational Approach to Self-Adjointness
- 3 The Fundamental Analytic Theorems of the Inverse Problem
- Appendix: Newtonian Systems
- A.1 Newton’s equations of motion
- A.2 Constraints
- A.3 Generalized coordinates
- A.4 Conservative systems
- A.5 Dissipative systems
- A.6 Dynamical systems
- A.7 The fundamental form of the equations of motion in configuration space
- Charts
- A.1 Galilean relativity
- A.2 Ignorable coordinates and conservation laws
- A.3 Impulsive motion
- A.4 Arrow of time and entropy
- A.5 Gauss principle of least constraint
- A.6 The Gibbs-Appel equations
- A.7 Virial theorem
- A.8 Liouville’s theorem for conservative systems
- A.9 Generalizations of Liouville’s theorem to dynamical systems
- A.10 The method of Lagrange undetermined multipliers
- A.11 Geometric approach to Newtonian systems
- A.12 Tensor calculus for linear coordinate transformations
- A.13 Tensor calculus for nonlinear coordinate transformations
- A.14 Dynamical systems in curvilinear coordinates
- Examples
- Problems
- References