Generalized Momenta

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

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