# Generalized Momenta

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Generalized Momenta

physical quantities *p _{i}* that are defined by the formulas

*p*= ∂

_{i}*T*/∂

*q*or

_{i}*p*= ∂

_{i}*L*/∂

*q*, where

_{i}*T*is the kinetic energy and

*L*is the Lagrangian function of a given mechanical system, and that depend on the generalized coordinates

*q*, generalized velocities

_{i}*q*, and time

_{i}*t*. The dimensions of the generalized momenta depend on the dimensions of the generalized coordinates. For example, if the

*q*are lengths, then the

_{i}*p*have dimensions of ordinary momentum, that is, the product of mass and velocity. If, however, the

_{i}*q*are angles (a dimensionless quantity), then the

_{i}*p*have dimensions of angular momentum.

_{i}The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.