Analytical Mechanics FROM THE PUBLISHER
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.
FROM THE CRITICS
Booknews
First published in 1788, about a century after Newton's "Principia
Mathematica", the French mathematician's most famous work marked the
culmination of a line of research devoted to recasting Newton's
synthetic, geometric methods in the analytic style of the Leibnizian
calculus. It used the principle of virtual work as the foundation for
all of mechanics, and so integrated statics, hydrostatics, dynamics,
and hydrodynamics. It also introduced a fictitious constraint force
to enforce an algebraic relation between the coordinates of the parts
of a continuous body or between various bodies. From there Lagrange
used his own calculus of variation to vary the configuration of a
system in statics or the path of a system in dynamics in order to
obtain the governing differential equation. The work, here translated
from the third edition, remains important for scientists and is also
of interest to historians of science. No index.
Annotation c. by Book News, Inc., Portland, Or.
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