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Q55Section II (Mathematics)55 of 145

Legendre transform of a pendulum-type Lagrangian

If Lagrangian of a system is L(θ,θ˙)=12m(l2θ˙2−glθ2)L(\theta,\dot\theta)=\frac12m(l^2\dot\theta^2-gl\theta^2), where g,lg,l are constants. Then the Hamiltonian of the system is:

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