"Mechanical Systems, Classical Models. Volume III: Analytical Mechanics" by Petre P. Teodorescu (Repost)

The guideline of the book is precisely the mathematical model of mechanics. Starting from the particle (the simplest problem) and finishing with the study of dynamical systems, the book covers a wide number of problems.
This volume deals with analytical mechanics.

The book is divided in three volumes:
I. Particle mechanics.
II. Mechanics of discrete and continuous systems.
III. Analytical mechanics.


Contents III. Analytical mechanics
Preface
18. Lagrangian Mechanics
1. Preliminary Results
1.1 Introductory Notions
1.2 Differential Principles of Mechanics
2. Lagrange’s Equations
2.1 Space of Configurations
2.2 Lagrange’s Equations of Second Kind
2.3 Transformations. First Integrals
3. Other Problems Concerning Lagrange’s Equations
3.1 New Forms of Lagrange’s Equations
3.2 Applications
19. Hamiltonian Mechanics
1. Hamilton’s Equations
1.1 General Results
1.2 Lagrange’s Brackets. Poisson’s Brackets
1.3 Applications
2. The Hamilton–Jacobi Method
2.1 General Results
2.2 Systems of Equations with Separate Variables
2.3 Applications
20. Variational Principles. Canonical Transformations
1. Variational Principles
1.1 Mathematical Preliminaries
1.2 The General Integral Principle
1.3 Hamilton’s Principle
1.4 Maupertuis’s Principle. Other Variational Principles
1.5 Continuous Mechanical Systems
2. Canonical Transformations
2.1 General Considerations. Conditions of Canonicity
2.2 Structure of Canonical Transformations. Properties
3. Symmetry Transformations. Noether’s Theorem. Conservation Laws
3.1 Symmetry Transformations. Noether’s Theorem
3.2 Lie Groups
3.3 Space-Time Symmetries. Conservation Laws
21. Other Considerations on Analytical Methods in Dynamics of Discrete Mechanical Systems
1. Integral Invariants. Ergodic Theorems
1.1 Integral Invariants of Order 2s
1.2 Invariants of First Order
1.3 Ergodic Theorems
2. Periodic Motions. Action-Angle Variables
2.1 Periodic Motions. Quasi-Periodic Motions
2.2 Action-Angle Variables
2.3 Adiabatic Invariance
3. Methods of Exterior Differential Calculus. Elements of Invariantive Mechanics
3.1 Methods of Exterior Differential Calculus
3.2 Elements of Invariantive Mechanics
3.3 Applications
4. Formalisms in the Dynamics of Mechanical Systems
4.1 Formalisms in Spaces with s + 1 Dimensions
4.2 Formalism in Spaces with 2s +1 or with 2s +2 Dimensions
4.3 Notions on the Inverse Problem of Mechanics and the Birkhoffian Formalism
5. Control Systems
5.1 Control Systems
5.2 Optimal Trajectories
22. Dynamics of Non-holonomic Mechanical Systems
1. Kinematics of Non-holonomic Mechanical Systems
1.1 General Considerations
1.2 Conditions of Holonomy. Quasi-co-ordinates. Non-holonomic Spaces
2. Lagrange’s Equations. Other Equations of Motion
2.1 Motion of a Rigid Solid on a Fixed Surface
2.2 Lagrange’s Equations
2.3 Applications
2.4 Other Equations of Motion
3. Gibbs–Appell Equations
3.1 Gibbs–Appell Equations of Motion
3.2 Applications
4. Other Problems on the Dynamics of Non-holonomic Mechanical Systems
4.1 Collisions 491
4.2 First Integrals of the Equations of Motion
23. Stability and Vibrations
1. Stability of Mechanical Systems
1.1 Stability of Equilibrium
1.2 Stability of Motion
1.3 Applications
2. Vibrations of Mechanical Systems
2.1 Small Free Oscillations About a Stable Position of Equilibrium
2.2 Small Forced Oscillations
2.3 Non-linear Vibrations
2.4 Applications
24. Dynamical Systems. Catastrophes and Chaos
1. Continuous and Discrete Dynamical Systems
1.1 Continuous Linear Dynamical Systems
1.2 Non-linear Differential Equations and Systems of Non-linear Differential Equations
1.3 Discrete Linear Dynamical Systems
2. Elements of the Theory of Catastrophes
2.1 Ramifications
2.2 Elementary Catastrophes
3. Periodic Solutions. Global Bifurcations
3.1 Periodic Solutions
3.2 Global Bifurcations
4. Fractals. Chaotic Motions
4.1 Fractals
4.2 Chaotic Motions
Subject Index
Name Index
Bibliography