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Analytical Mechanics : Boston Studies in the Philosophy and History of Science - Joseph Louis Lagrange

Analytical Mechanics

Boston Studies in the Philosophy and History of Science

Hardcover

Published: 31st December 1996
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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.

Preface
Translators'
Introduction
Excerpt
Preface
Statics
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
Dynamics
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
Dynamics
Detailed Table of Contents
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
Notes
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792343493
ISBN-10: 0792343492
Series: Boston Studies in the Philosophy and History of Science
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 594
Published: 31st December 1996
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 4.24
Weight (kg): 2.37