Extremisation of Hamiltonian of Eight DoF Rotor System

Abstract

The orbital path (spatial coordinates) variation of a rotor dynamic system under the influence of gyroscopic couple is not a trivial problem to predict. This comprises of computations to obtain the movement of the mass centre of the rotor to the whirling orbit radius with imposed gyroscopic moment under the principle of least action which necessarily estimates the Lagrangian of the rotor system at a given instant of time and thereby arriving at the Hamiltonian. This approach, unlike the usual Newton’s laws of motions procedure, is not very common. The orbital path of the rotor is obtained for an 8 degree of freedom (DoF) rotor system, satisfying the Hamiltonian principle of least action (extremisation) using Monte-Carlo simulation. The centre of the whirling orbit of a rotor system which is the geometric center of a rotor system under the influence of gyroscopic moment is the path of least distance not the path of least time, hence the rotor center moves in a straight line to reach the whirling radius of the orbital path.