Analytical Mechanics 1997th Edition by J.L. Lagrange, ISBN-13: 978-0792343493
[PDF eBook eTextbook]
- Publisher: Springer; 1997th edition (December 31, 1996)
- Language: English
- 639 pages
- ISBN-10: 0792343492
- ISBN-13: 978-0792343493
The English translation of Lagrange’s Mecanique Analytique (Lagrange’s Mecanique Analytique) appeared early in 1788 almost exactly one century after the publication of Newton’s Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton’s synthetic, geometric 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 authors 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 of 1736.
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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