cyclic variable

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A cyclic variable is a generalized coordinate that does not appear explicitly in the Lagrangian (although its time derivative might). For such a variable, the canonically conjugate momentum is conserved:

\frac{\partial L}{\partial q_c} = 0 \implies \frac{d}{dt} \left(\frac{\partial L}{\partial \dot{q}_c} \right) = \frac{dp_c}{dt} = 0\,.

back to Hamilton's principle
back to Lagrangian mechanics
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