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Hamiltonian
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- TL;DR Summary
- on applying the Euler Lagrange equation onto a system what exactly are you solving for and what is the significance of the solution you get?
I am new to Lagrangian mechanics and I have gone through basic examples of solving the Euler Lagrange equation for simple pendulums or projectiles and things like that. But I am unable to understand what we are exactly solving the equation for or what is the significance of the differential equation you end up with.
for example, if you consider a simple pendulum of mass m and length l
you get the lagrangian as $$L = (1/2)(mgl)\dot \theta^2 - mgl + mglcos\theta$$
and finally solving the Euler Lagrange equation gives you $$ 0 = \ddot \theta + (g\theta)/l$$
what is the significance of this solution?
for example, if you consider a simple pendulum of mass m and length l
you get the lagrangian as $$L = (1/2)(mgl)\dot \theta^2 - mgl + mglcos\theta$$
and finally solving the Euler Lagrange equation gives you $$ 0 = \ddot \theta + (g\theta)/l$$
what is the significance of this solution?