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By A Wolf

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G eneral P r in c ip l e s The earlier writers on mechanics had been satisfied, for the most part, with solving numerous isolated problems in all branches o f applied mathematics. As each problem had to be attacked in a different way, by the employment o f special artifices, only men o f the highest mathematical talent could apply themselves to mechanical problems with any hope o f success. During the eighteenth century, however, a number o f general mechanical principles were formulated which could be applied to whole classes o f problems.

Then the system is in equilibrium i f P-^Px + + . . = o, or, more shortly, S = o, which is the fundamental equation o f statics. {X dx-Y T dy^ -Zdz) = 0 , where X, T and ^ are the three components o f the force acting upon a typical particle, and dx, dj), dz, the three components o f the virtual displacement o f that particle. The derivation o f the corresponding formulae o f dynamics from the principle o f virtual displacements, in combination with D ’Alembert’s Principle, is effected somewhat as follows: Consider a system o f particles whose masses are m^.

From an early age he displayed marked gifts in mathe­ matics and philosophy, and he became a member o f the Paris and Berlin Academies. But he declined tempting invitations from Frederick the Great and from the Empress Catherine II, remaining in France until his death. D ’Alembert was only twenty-six years old when his Traite de la dynamique (Paris, 1743) was published. (For an annotated German translation, see Ostwald’s Klassiker, No. ) The book is a landmark in the development o f mechanics, embodying as it does a principle as simple and as fundamental for the motion of bodies as is the principle o f virtual velocities for their equilibrium.

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


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