If L(qj,dot qj,t) and H(pj,qj,t) are the Lagrangian and Hamiltonian, then Lagrange's equations of motion frac ddt(partial L/partialdot qj)-partial L/partial qj=0 can also be represented as:

Q97Section II (Mathematics)97 of 180

Mechanics — the energy relation is a consequence, not a restatement

If $L(q_j,\dot q_j,t)$ and $H(p_j,q_j,t)$ are the Lagrangian and Hamiltonian, then Lagrange's equations of motion $\frac d{dt}\bigl(\frac{\partial L}{\partial\dot q_j}\bigr)-\frac{\partial L}{\partial q_j}=0$ can also be represented as:

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