The governor for an engine, consists of two balls, each of mass m, attached by light arms to sleeves on a rotating rod. The upper sleeve is fixed to the rod, and the lower one of mass M is free to move up and down. Assume the arms to be massless and the angular velocity w to be costant. Find the Lagrangian and Hamiltonian functions, and obtain Hamilton's equations of motion describing the system. Solve for the angle theta at which the arms would stop waving, and obtain the frequency of small oscillations about the steady value. shown in figure 5.5
This solution looks at the flyball governor situation and calculates the angle theta at which the arms would stop waving as well as the frequency of the small oscillations about the steady value using concepts of equilibrium and oscillation frequency. All steps are shown with brief explanations.