Generalized Forces

Modelling and Simulation Lecture Notes.pdf Ch 2.4

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Generalized force $Q_{ij}$ acting on Generalized Coordinates $q_i$ due to a force $F_j$ is

$$Q_{ij}=F_j^T\frac{\partial p_j}{\partial q}$$

Where $p_j$ is the point where $F_j$ is applied.

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Applied in the equations of motion (Euler-Lagrange Equation) gives

$$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{q}}\right)-\frac{\partial L}{\partial q}=\sum _j{Q}_j$$