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Physics
Classical Physics
Mechanics
2 Different Ways to Write Potential Energy of a Pendulum
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[QUOTE="vanhees71, post: 6058317, member: 260864"] Just another remark. The Lagrangian is not a physical observable but it's used to define the action for Hamilton's action principle. Thus two Lagrangians ##L(q,\dot{q},t)## and ##L'(q,\dot{q},t)## are completely equivalent if $$L'(q,\dot{q},t)=L(q,\dot{q},t)+\frac{\mathrm{d}}{\mathrm{d} t} \Omega(q,t)=L(q,\dot{q},t)+\dot{q} \cdot \vec{\nabla}_q \Omega(q,t) + \partial_t \Omega(q,t),$$ because adding such a term leaves the variation of the action and thus the Euler-Lagrange equations invariant. This is a very important concept for the derivation of Noether's theorem. [/QUOTE]
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Classical Physics
Mechanics
2 Different Ways to Write Potential Energy of a Pendulum
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