Generalized forces

Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates. They are obtained from the applied forces, Fi, i=1,..., n, acting on a system that has its configuration defined in terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate. Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates. They are obtained from the applied forces, Fi, i=1,..., n, acting on a system that has its configuration defined in terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate. Generalized forces can be obtained from the computation of the virtual work, δW, of the applied forces.:265 The virtual work of the forces, Fi, acting on the particles Pi, i=1,..., n, is given by where δri is the virtual displacement of the particle Pi. Let the position vectors of each of the particles, ri, be a function of the generalized coordinates, qj, j=1,...,m. Then the virtual displacements δri are given by where δqj is the virtual displacement of the generalized coordinate qj.