History 2

A History of Science, Technology, and Philosophy in the by A Wolf

By A Wolf

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D ’Alembert’s Principle obviously relates the problems o f dynamics to investigations on equilibrium and the practical know­ ledge thereby obtained; it by no means makes experience superfluous. It serves as a model for the convenient solution o f problems, and, as Mach has pointed out, it promotes not so much insight into mechanical processes as the practical mastery o f them. THE P R IN C IP L E OF L E A S T A C T IO N A n important dynamical generalization first partially formulated in the eighteenth century is that known as the Principle o f Least Action, or, more accurately, o f Stationary Action.

Action has come to play a fundamentally important part in twentieth-century Physics; it is an absolute quantity, independent o f the way in which the space-time continuum is analysed by any particular observer; and the discovery o f its atomicity is the basis o f the Quantum Theory. (See A. ) euler’s e q u a t io n s Euler introduced into Dynamics the important general equations which still bear his name and which relate to the motion o f a rigid body about a fixed point or about its mass-centre {Mem.

Thus two in­ dependent methods o f attacking any given physical problem were indicated, one direct and the other indirect, which tended to confirm each other, and so led to a higher degree o f confidence in the solution. For example, in determining the curvature o f a rope suspended at both ends, the problem could be solved either directly by considering the action exerted by gravity upon the rope, or indirectly by employing the method o f maxima and minima to define the form which the rope must assume in order that its centre o f gravity should lie at as low a level as possible.

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