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Lagrangian & Hamiltonian Formulations question bank (Classical Mechanics & Electrodynamics)

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Q1.
If a generalized coordinate q_k is cyclic (ignorable) in the Lagrangian L(q, q_dot, t), meaning dL/dq_k = 0, what can be concluded about its conjugate momentum p_k?

(A)
p_k is a constant of motion (conserved)
(B)
p_k must be identically zero
(C)
p_k increases linearly with time
(D)
p_k equals the Hamiltonian
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