Lagrange J.L. Analytical Mechanics

Translated from the Mécanique analytique, novelle édition of 1811 — Dordrecht: Springer Netherlands, 1997. — 634 p. — ISBN 978-90-481-4779-3.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.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