- Generalized force
The idea of a

**Generalized Force**is a concept stemming fromLagrangian mechanics . It is a consequence of the application ofgeneralized coordinates to a system undergoing acceleration.When a particle undergoes a

virtual displacement $delta\; mathbf\{r\}$ under the influence of a force $mathbf\{F\}$ thevirtual work done by that force is given by:

$delta\; W\; =\; mathbf\{F\}\; cdot\; delta\; mathbf\{r\}\; =\; sum\_\{i\}\; F\_i\; delta\; x\_i$.Translating to

generalized coordinates :

$delta\; W\; =\; sum\_\{i\}\; (sum\_\{j=1\}^n\; F\_i\; frac\; \{partial\; x\_i\}\{partial\; q\_j\}\; delta\; q\_j)$,and by reversing the order of summation we get

$delta\; W\; =\; sum\_\{j=1\}^n\; (\; sum\_\{i\}F\_i\; frac\; \{partial\; x\_i\}\{partial\; q\_j\})delta\; q\_j$.It is from this formulation that the idea of a generalized force stems. The above equation can be written as

$delta\; W\; =\; sum\_\{j=1\}^n\; (Q\_j)delta\; q\_j$where

$Q\_j\; =\; sum\_\{i\}F\_i\; frac\; \{partial\; x\_i\}\{partial\; q\_j\}$is called the generalized force associated with the coordinate $q\_j$.

Since $Q\_jq\_j$ has the dimension of work, $Q\_j$ will have the dimension of

force if $q\_j$ is a distance, and the dimension oftorque if $q\_j$ is an angle.**ee also***

Lagrangian mechanics

*Generalized coordinates

*Degrees of freedom (physics and chemistry)

*Virtual work

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Generalized coordinates**— By deriving equations of motion in terms of a general set of generalized coordinates, the results found will be valid for any coordinate system that is ultimately specified. cite book |last=Torby |first=Bruce |title=Advanced Dynamics for… … Wikipedia**Generalized game theory**— is an extension of game theory to incorporate social theory concepts such as norm, value, belief, role, social relationship, and institution. The theory was developed by Tom R. Burns and has not had great influence beyond his immediate associates … Wikipedia**Force**— For other uses, see Force (disambiguation). See also: Forcing (disambiguation) Forces are also described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything that might cause a mass to accelerate … Wikipedia**Centrifugal force (planar motion)**— In classical mechanics, centrifugal force (from Latin centrum center and fugere to flee ) is one of the three so called inertial forces or fictitious forces that enter the equations of motion when Newton s laws are formulated in a non inertial… … Wikipedia**Centrifugal force**— Not to be confused with Centripetal force. Classical mechanics Newton s Second Law … Wikipedia**Centripetal force**— Not to be confused with Centrifugal force. Classical mechanics Newton s Second Law … Wikipedia**Fictitious force**— Classical mechanics Newton s Second Law History of classical mechanics … Wikipedia**Ponderomotive force**— In physics, a ponderomotive force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field. The ponderomotive force Fp is expressed by where e is the electrical charge of the particle, m is… … Wikipedia**Use of force**— The term use of force refers to the right of an individual or authority to settle conflicts or prevent certain actions by applying measures to either: a) dissuade another party from a particular course of action, or b) physically intervene to… … Wikipedia**Abraham-Lorentz-Dirac force**— In electrodynamics, the Abraham Lorentz Dirac force is the force experienced by a relativistic charged particle due to an electromagnetic field. It is a modification of the Abraham Lorentz force, which describes the same effect, but does not… … Wikipedia