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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^. . and whose co-ordinates are Z il ^2? J2j Za etc. Let the components o f the forces acting upon the several particles be X^, Tj, Xg, Tg, Z2) etc.

To act upon a connected system o f particles, and the corresponding virtual displacements in the directions o f the respective forces to be j&3 . . 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^.

Jean-le-Rond on the steps o f which he was found abandoned as an infant; and his surname o f Alembert, from his working-class foster-parents. His real parents appear to have been people o f high rank, and his father provided for his education. 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.

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