You're right, I completely messed up. My mistake was a mistake correcting a mistake. I had accidentally noticed that I wasn't supposed to take the derivative of the lagrangian with respect to the r because it was a constant, and mistakenly removed only half of it from my working out, thus the...
Hi, I've derived the equation of motion for a regular single pendulum, but do not know how to solve the differential equation.
I have the following:
r2θ''2=mg(cosθ-rsinθ)
The particular equation I would like to see solve is:
##\sin\theta\frac{d}{d\theta}(\sin\theta\frac{d\Theta}{d\theta})+\Theta(l(l+1)\sin\theta-m^2)##
The solution for this equation is the following associated laguerre polynomial...