Recent content by Michael Korobov

Hi, Can you please help me understand how the formula of energy decreasing during a sand leaking is obtained? One of possible solution to this problem, suggested in the textbook, states that when the bucket moves from x to x+dx (d is negative), there are two components responsible of energy...

Indeed, this was the only way to get consistent solution. Thanks!

Hi, Can anyone hint me if there is issue in the problem statement? Consistent answer can be obtained if one presumes that the trajectory of center mass is parabolic. Assuming this, the CM will land at distance L right to the axis of symmetry of parabola. But the problem tells about a rocket...

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...