16.61 Aerospace Dynamics Spring 2003 Principle of virtual Work m = mass of particle i R,- Constraint forces acting on the particle F- External forces acting on the particle 2 For static equilibrium (if all particles of the system are motionless in the inertial frame and if the vector sum of all forces acting on each particle is zero) R.+F=0 The virtual work for a system in static equilibrium is δW=∑(R,+F)·or=0 But virtual displacements must be perpendicular to constraint forces. so R.·6r=0 which implies that we have ∑F·br Principle of virtual work: The necessary and sufficient conditions for the static equilibrium of an initially motionless scleronomic system which is subject to workless bilateral constraints is that zero virtual work be done by the applied forces in moving through an arbitrary virtual displacement satisfying the constraints Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 Principle of Virtual Work mi = mass of particle i Ri = Constraint forces acting on the particle Fi = External forces acting on the particle ! For static equilibrium (if all particles of the system are motionless in the inertial frame and if the vector sum of all forces acting on each particle is zero) 0 R F i i + = The virtual work for a system in static equilibrium is ( ) 1 0 N i i i i δ δ W = = + ∑ R F • r = But virtual displacements must be perpendicular to constraint forces, so 0 i δ i R r • = , which implies that we have 1 0 N i i i δ = ∑F r • = Principle of virtual work: The necessary and sufficient conditions for the static equilibrium of an initially motionless scleronomic system which is subject to workless bilateral constraints is that zero virtual work be done by the applied forces in moving through an arbitrary virtual displacement satisfying the constraints. Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 6