generalized coordinate

This is a suitable choice of generalized coordinate for the system.

An example of a generalized coordinate is the angle that locates a point moving on a circle.

The space described above is commonly denoted (F) and is called generalized coordinate space for the following reason.

Generalized coordinate and generalized force: analogous conjugate variable pairs found in classical mechanics.

In particular, if the original generalized coordinate undergoes an oscillation or rotation of period , the corresponding action angle changes by .

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

As in Lagrangian mechanics, if a generalized coordinate does not appear in the Hamiltonian, its conjugate momentum component is conserved.

This shows that the parameter θ is a generalized coordinate that can be used in the same way as the Cartesian coordinates x and y to analyze the pendulum.

A simple pendulum has one generalized coordinate (the angular displacement ) and two constraints (the length of the string is constant and there is no motion along the z axis).

Following the generalized coordinate method of Vlasov, simple beam theory has been extended to treat torsional, distortional, and shear lag effects in straight, thin-walled box beams of uniform section.

The variable J is called the "action" of the generalized coordinate q; the corresponding canonical variable conjugate to J is its "angle" w, for reasons described more fully under action-angle coordinates.

Performing a Legendre transformation on the generalized coordinate Lagrangian L(q, dq/dt, t) obtains the generalized momenta Lagrangian L'(p, dp/dt, t) in terms of the original Lagrangian, as well the EL equations in terms of the generalized momenta.