Given that pendulum of mass m and length l with angular displacement θ from the vertical.
From the geometry, the expressions for the kinetic and potential energies are,
K = 1/ 2 (mlθ )2
U = mgl(1 − cos θ)
Accordingly,
L = K − U = 1/2(ml2θ2− mgl(1 − cos θ).
The
∂L/∂θ = −mglsin (θ)
and
∂L/∂θ = ml2θ
so
d/dt( ∂L/∂θ ) = ml2θ
and finally solving for θ ,
we have
θ = −( g sin θ ) / l. |
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