Analytical Mechanics: Translated from the Mécanique analytique, novelle édition of 1811

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. Front Matter....Pages i-10 The Various Principles of Statics....Pages 11-26 A General Formula of Statics and its Application to the Equilibrium of an Arbitrary System of Forces....Pages 26-37 The General Properties of Equilibrium of a System of Bodies Deduced from the Preceding Formula....Pages 37-59 A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II....Pages 60-82 The Solution of Various Problems of Statics....Pages 82-136 The Principles of Hydrostatics....Pages 136-140 The Equilibrium of Incompressible Fluids....Pages 140-163 The Equilibrium of Compressible and Elastic Fluids....Pages 164-167 The Various Principles of Dynamics....Pages 169-184 A General Formula of Dynamics for the Motion of a System of Bodies Moved by Arbitrary Forces....Pages 184-190 General Properties of Motion Deduced from the Preceding Formula....Pages 190-223 Differential Equations for the Solution of All Problems of Dynamics....Pages 223-236 A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants....Pages 236-252 The Very Small Oscillations of an Arbitrary System of Bodies....Pages 253-305 The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction....Pages 311-442 The Motion of Constrained Bodies Which Interact in an Arbitrary Fashion....Pages 442-467 Rotational Motion....Pages 467-517 The Principles of Hydrodynamics....Pages 517-521 The Motion of Incompressible Fluids....Pages 521-560 The Motion of Compressible and Elastic Fluids....Pages 560-573 Back Matter....Pages 575-594 J. L. Lagrange is a name well known to students in all branches of mathematics and applied mathematics. But by far his most famous work deals with mechanics - the Mecanique Analytique. In this work, he used the Principle of Virtual Work as the foundation for all of mechanics and thereby brought together statics, hydrostatics, dynamics and hydrodynamics. His approach differed significantly from the mechanics of Newton and the physical approach to mechanics of Laplace and Poisson. The difference is due primarily to the introduction by Lagrange of a fictitious constraint force. The purpose of the constraint force is to enforce an algebraic relation between the coordinates of the parts of a continuous body or between various bodies. Moreover, the physical origin of this force does not have to be known. From this point, Lagrange utilizes the methodology of the Calculus of Variations - a methodology which he himself developed - to vary the configuration of a system in statics or the path of a system in dynamics in order to obtain the governing differential equations. Audience: Historians of science, mathematicians, physicists and engineers, and scholars specializing in classical mechanics, celestial mechanics, mathematics of mechanics and mechanics in general.