Analytical Mechanics

Analytical Mechanics

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to the English translation of Lagrange's Mecanique Analytique Lagrange's Mecanique Analytique appeared early in 1788 almost exactly one cen- tury after the publication of Newton's Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet- ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au- thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and methods to investigate problems in constrained interaction, fluid flow, elasticity, strength of materials and the operation of machines. The Mecanique Analytique was a remarkable work of compilation that became a fundamental reference for subsequent research in exact science. During the eighteenth century there was a considerable emphasis on extending the domain of analysis and algorithmic calculation, on reducing the dependence of advanced mathematics on geometrical intuition and diagrammatic aids.
The analytical style that characterizes the Mecanique Analytique was evident in La- grange's original derivation in 1755 of the 8-algorithm in the calculus of variations. It was expressed in his consistent attempts during the 1770s to prove theorems of mathematics and mechanics that had previously been obtained synthetically. The scope and distinctiveness of his 1788 treatise are evident if one compares it with an earlier work of similar outlook, Euler's Mechanica sive Motus Scientia Analyt- 1 ice Exposita of 1736.
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Product details

  • Hardback | 594 pages
  • 165.1 x 241.3 x 45.7mm | 1,247.39g
  • Dordrecht, Netherlands
  • English
  • 1997 ed.
  • XLV, 594 p.
  • 0792343492
  • 9780792343493

Back cover copy

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.
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Table of contents

Preface; Craig G. Fraser. Translators' Introduction. Excerpt. Volume I. Preface. Part I: Statics. I. The Various Principles of Statics. II. A General Formula of Statics and Its Application to the Equilibrium of an Arbitrary System of Forces. III. The General Properties of Equilibrium of A System of Bodies Deduced from the Preceding Formula. IV. A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II. V. The Solution of Various Problems of Statics. VI. The Principles of Hydrostatics. VII. The Equilibrium of Incompressible Fluids. VIII. The Equilibrium of Compressible and Elastic Fluids. Part II: Dynamics. I. The Various Principles of Dynamics. II. A General Formula of Dynamics for the Motion of A System of Bodies Moved by Arbitrary Forces. III. General Properties of Motion Deduced from the Preceding Formula. IV. Differential Equations for the Solution of all Problems of Dynamics. V. A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants. VI. The Very Small Oscillations of an Arbitrary System of Bodies. Volume II: Dynamics. Detailed Table of Contents. VII. The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction. VIII. The Motion of Constrained Bodies which Interact in an Arbitrary Fashion. IX. Rotational Motion. X. The Principles of Hydrodynamics. XI. The Motion of Incompressible Fluids. XII. The Motion of Compressible and Elastic Fluids. Notes.
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