Local bifractionin in torque free rigid body motion

Abstract

Local bifurcation of the attitudinal dynamics of the torque free rigid body motion is discussed. Hamiltonian formalism is used to express equations of motion. To simplify attitudinal dynamics of a rigid body, six dimensional state space is reduced to a two dimensional one by Andoyer canonical transformation. Non-dimensional parameters of the system are defined and the effects of change in these parameters on the structural stability and the equilibrium points of the reduced space are discussed. The Poincaré surface of the section in the reduced phase space and heteroclinic orbits are derived. Based on the non-dimensional parameters of the system, two and three dimensional bifurcation diagrams are achieved. This study shows that various types of structural stability can be achieved for torque free rigid body attitudinal dynamics by changing relative magnitudes of the principal moments of inertia. These results are helpful when the chaotic behavior of a rigid body under perturbation is considered