Looks like I understood the problem.
The position of the stick is not the dynamical variable as it's a given function of time not depending on initial conditions therefore shouldn't be considered.
So, the system effectively has only one degree of freedom - bead's position on the wire.
Thanks!
This is the exact solution from Morin.
The equation 6.142 corresponds to the second equation in my question
If we presume ##\omega=\dot \theta## then we have to take partial derivative over it into account, But this doesn't happen.
Looks like I'm missing something obvious...
Hi,
In David Morin's "Introduction to classical mechanics", Problem 6.8, when deriving Hamiltonian of the bead rotating on a horizontal stick with constant angular speed, the Lagrangian derivative over angular speed isn't included.
Why is that?
Specifically, the Lagrangian takes form...