Generalized Momenta

Generalized Momenta

 

physical quantities pi that are defined by the formulas pi = ∂T/∂qi or pi = ∂L/∂qi, where T is the kinetic energy and L is the Lagrangian function of a given mechanical system, and that depend on the generalized coordinates qi, generalized velocities qi, and time t. The dimensions of the generalized momenta depend on the dimensions of the generalized coordinates. For example, if the qi are lengths, then the pi have dimensions of ordinary momentum, that is, the product of mass and velocity. If, however, the qi are angles (a dimensionless quantity), then the pi have dimensions of angular momentum.

References in periodicals archive ?
z] should be expressed in terms of generalized momenta [P.
The expression for Hamiltonian through generalized momenta is given in (57), and relation (57') sets the energy of the particle for flat Minkowski space.

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