Analytical mechanics for students of physics and engineering . etc., due to the virtual displacementds. But since the left-hand member of the last equationis an infinitesimal of the second order while the terms of theright-hand member are infinitesimals of the first order wecan neglect the left-hand member and write Fi dsj. + F2ds2 + ? • • + = 0. (VIII) Equation (VIII) states: when a particle which is in equi-librium is given a virtual displacement the total amount of workdone by the forces acting upon the particle vanishes. This isthe principle of virtual work. The principle of virtual work i
Analytical mechanics for students of physics and engineering . etc., due to the virtual displacementds. But since the left-hand member of the last equationis an infinitesimal of the second order while the terms of theright-hand member are infinitesimals of the first order wecan neglect the left-hand member and write Fi dsj. + F2ds2 + ? • • + = 0. (VIII) Equation (VIII) states: when a particle which is in equi-librium is given a virtual displacement the total amount of workdone by the forces acting upon the particle vanishes. This isthe principle of virtual work. The principle of virtual work is applicable not only toparticles, but also to any system which is in the system is acted upon by torques as well as forces,then the sum of the work done by the virtual torques andthe virtual force- vanishes: Fxdsl + F2ds2 + ? ? ? +Gidei + Gidei+ •••-(>. IX 182 ANALYTICAL MECHANICS. ILLUSTRATIVE EXAMPLES. 1. Supposing the weights in Fig. 98 to be in equilibrium and the con-tacts to be smooth, rind the relation between the two weights If Ui is given a virtual displace-ment towards the left along the in-clined plane, then the virtual work is - T ds + Wi • ds sin a + N • 0 = 0,or T = W\ sin a. But T = W2. Therefore W2 = Witana. 2. Two uniform rods of equal weight W and equal length a are jointedat one end and placed, as shown in Fig. 99, in a vertical plane on a smoothhorizontal table. A string of length I joins the middle points of therods. Find the tension of the string. The following forces act upon each rod — the weight of the rod, thepull of the string, the reaction at the joint, and the reaction of the a slighl displacement to be given to the system by pressing down-ward at the joint. The work done by the force which produced the dis-placement equals the sum of the work done by the other forces which actupon the rods during the displace-men
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