terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate...

{q}}}}\right),} is the generalized force acting on this one degree of freedom system. If the mechanical system is defined by m generalized coordinates, qj,...

Given this vk, the kinetic energy in generalized coordinates depends on the generalized velocities, generalized coordinates, and time if the position...

reference state. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes...

system, known as Lagrange's equations or the generalized equations of motion. If the generalized forces Qj are derivable from a potential energy V(q1...

in the context as generalized coordinates. The kinetic and potential energies of the system are expressed using these generalized coordinates or momenta...

(condensation). Only when these "forces" equilibrate is equilibrium obtained. Generalized coordinate and generalized force: analogous conjugate variable...

{\theta }}^{2}.} The generalized coordinates of the system are θ {\displaystyle \theta } and x {\displaystyle x} , each has a generalized force. On the x {\displaystyle...

ISBN 978-0-486-65067-8. For a description of generalized coordinates, see Ahmed A. Shabana (2003). "Generalized coordinates and kinematic constraints". Dynamics...

the forces of constraint vanish. That is to say that the generalized forces Q j {\displaystyle \mathbf {Q} _{j}} need not include constraint forces. It...