Analytical Mechanics [electronic resource] : Translated from the Mécanique analytique, novelle édition of 1811

Analytical Mechanics: Translated from the Mécanique analytique, novelle édition of 1811
Author: Auguste Boissonnade, Victor N. Vagliente, J. L. Lagrange
Published by Springer Netherlands
ISBN: 978-90-481-4779-3
DOI: 10.1007/978-94-015-8903-1

Table of Contents:

• The Various Principles of Statics
• A General Formula of Statics and its Application to the Equilibrium of an Arbitrary System of Forces
• The General Properties of Equilibrium of a System of Bodies Deduced from the Preceding Formula
• A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II
• The Solution of Various Problems of Statics
• The Principles of Hydrostatics
• The Equilibrium of Incompressible Fluids
• The Equilibrium of Compressible and Elastic Fluids
• The Various Principles of Dynamics
• A General Formula of Dynamics for the Motion of a System of Bodies Moved by Arbitrary Forces
• General Properties of Motion Deduced from the Preceding Formula
• Differential Equations for the Solution of All Problems of Dynamics
• A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants
• The Very Small Oscillations of an Arbitrary System of Bodies
• The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction
• The Motion of Constrained Bodies Which Interact in an Arbitrary Fashion
• Rotational Motion
• The Principles of Hydrodynamics
• The Motion of Incompressible Fluids
• The Motion of Compressible and Elastic Fluids

The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations
Section I -- The Various Principles of Statics -- Section II -- A General Formula of Statics and its Application to the Equilibrium of an Arbitrary System of Forces -- Section III -- The General Properties of Equilibrium of a System of Bodies Deduced from the Preceding Formula -- Section IV. A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II -- Section V -- The Solution of Various Problems of Statics -- Section VI. The Principles of Hydrostatics -- Section VII. The Equilibrium of Incompressible Fluids -- Section VIII. The Equilibrium of Compressible and Elastic Fluids -- Section I. The Various Principles of Dynamics -- Section II. A General Formula of Dynamics for the Motion of a System of Bodies Moved by Arbitrary Forces -- Section III. General Properties of Motion Deduced from the Preceding Formula -- Section IV. Differential Equations for the Solution of All Problems of Dynamics -- Section V.A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants -- Section VI. The Very Small Oscillations of an Arbitrary System of Bodies -- Section VII. The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction -- Section VIII. The Motion of Constrained Bodies Which Interact in an Arbitrary Fashion -- Section IX. Rotational Motion -- Section X. The Principles of Hydrodynamics -- Section XI. The Motion of Incompressible Fluids -- Section XII. The Motion of Compressible And Elastic Fluids