generalized force

The generalized force component of this pair is the chemical potential.

Here the are the external variables and the the corresponding generalized forces.

The average defining the generalized force can now be written:

The generalized force for a system known to be in energy eigenstate is given by:

The terms Q are called the generalized forces associated with the virtual displacement δr.

It is not uncommonly called the generalized force.

That is to say that the generalized forces need not include constraint forces.

The connection between "generalized forces" and Newtonian forces varies with the choice of coordinates.

The generalized forces may be non-conservative, provided they satisfy D'Alembert's principle.

Expressed using equations, the exact relationship between generalized force and generalized potential is as follows:

Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates.

That is, one should avoid following Hildebrand when he says (p. 155) "we deal always with generalized forces, velocities accelerations, and momenta."

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

The pressure is the intensive generalized force, while the volume is the extensive generalized displacement:

The generalized momenta can be written in terms of the generalized forces in the same way as Newton's second law:

Here, the temperature, pressure, and chemical potential are the generalized forces, which drive the generalized changes in entropy, volume, and particle number respectively.

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

The generalized force for a rotation is the torque N, since the work done for an infinitesimal rotation is .

Within this formulation the motion is described in terms of generalized forces, using in place of Newton's laws the Euler-Lagrange equations.

Each term is composed of an intensive variable (a generalized force) and its conjugate infinitesimal extensive variable (a generalized displacement).

The pressure acts as a generalized force - pressure differences force a change in volume, and their product is the energy lost by the system due to mechanical work.

Just as the potential energy can be written as a quadratic form in the internal coordinates, so it can also be written in terms of generalized forces.

This equation is used in Lagrangian mechanics to relate generalized coordinates, q, to virtual work, δW, and generalized forces, Q.

An improved instrumentation scheme has been designed and tested for measuring the generalized forces occurring within armour units in a physical model of a breakwater subjected to wave action.

The vector f represents the generalized forces and the scalar V(q) represents the potential energy, both of which are functions of the generalized coordinates q.