Cryptic statement from my textbook

[dEdt]

This paragraph comes right after the authors derived the Hamiltonian of a rotating system, $H=H_{\omega=0}-\omega l_z$:

"The noninertial effects of rotation would lead to a considerably more complicated form using Lagrangian instead of Hamiltonian dynamics. The simplicity of the Hamiltonian is not an accident, nor is it accidental that the dynamical quantity $l_z$ appears in it."

Unfortunately, the authors don't explain why rotation is more easily handled with Hamiltonians than with Lagrangians, nor why angular momentum appears in the equations. Can anyone help elucidate what they mean?

 

[Adrmay]

The reason rotation is more easily handled with Hamiltonians than with Lagrangians is because Hamiltonians are based on energy conservation principles, which are ideal for describing rotational motion. Hamiltonians also allow one to express the equations of motion in terms of the angular momentum vector of the system, rather than the individual components of the angular momentum (such as l_z). This makes it much easier to solve the equations of motion and understand the behavior of the system. Additionally, the Hamiltonian formulation allows one to consider the effects of noninertial forces arising from rotation, such as centrifugal and Coriolis forces, more easily than with a Lagrangian formulation.