terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate...
5 KB (820 words) - 05:03, 28 October 2023
Rigid body dynamics (section Generalized forces)
{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,...
42 KB (5,759 words) - 10:46, 30 June 2024
Given this vk, the kinetic energy in generalized coordinates depends on the generalized velocities, generalized coordinates, and time if the position...
90 KB (14,229 words) - 15:08, 6 August 2024
reference state. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes...
28 KB (4,543 words) - 17:53, 19 August 2024
Virtual work (section Generalized inertia forces)
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...
45 KB (6,342 words) - 14:22, 20 August 2024
in the context as generalized coordinates. The kinetic and potential energies of the system are expressed using these generalized coordinates or momenta...
40 KB (5,759 words) - 04:26, 12 February 2024
(condensation). Only when these "forces" equilibrate is equilibrium obtained. Generalized coordinate and generalized force: analogous conjugate variable...
12 KB (1,636 words) - 07:52, 6 January 2023
{\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...
28 KB (4,447 words) - 17:29, 6 June 2024
Centrifugal force (redirect from Centrifugal forces)
ISBN 978-0-486-65067-8. For a description of generalized coordinates, see Ahmed A. Shabana (2003). "Generalized coordinates and kinematic constraints". Dynamics...
44 KB (5,725 words) - 15:21, 11 August 2024
D'Alembert's principle (redirect from D'Alembert forces)
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...
15 KB (2,389 words) - 15:04, 19 March 2024