A note on virtual displacements

There are several definitions of virtual displacement. Here are some exampl es from the literature: 1) A set of infinitesimal displacements such that t he geometrical boundary conditions are not violated (Washizu, [6]); An infi nitesimal displacement in the direction of the tangent to the path of movin g particle (Timoshenko and Young, [5]); 3) Any arbitrary infinitesimal chan ge of the coordinates of particles, consistent with the forces and constrai nts imposed on Me system at the given instant t (Goldstein, [2]; 4) Arbitra ry increments of displacements which satisfy kinematic boundary conditions (Oden, [4]); 5) Virtual displacements and their derivatives must be square integrable. Additionally, virtual displacements have to be equal zero where the actual displecements are prescribed (Becker, Carey, Oden, [1] and Hugh es, [3]). It is shown in [1] that virtual displacemnts may be arbitrarly large. In th e present contribution the principle of virtual displacements for the syste m of rigid bodies is derived using a novel definition of virtual displaceme nt: virtual displacemet is an arbitrary linear part of kinematically admiss ible displacement. Such definition corresponds to definitions given in [1] and [3]. An example of influence line determination is shown.