Symmetrization of some linear conservative nonself-adjoint systems

Abstract

We derive here equivalent self-adjoint systems for conservative systems of the second kind. Existence of the symmetrized systems confirms that certain conservative systems of the second kind behave as a true conservative system. In this way, study of stability can be carried out on the symmetrized system. In general, it is easier to study a self-adjoint system than a nonself-adjoint system. For the conservative system of the second kind, including the Pflüger column, we also presented a lower bound self-adjoint system. For a linear conservative gyroscopic system, we gave a zero parameter sufficient condition for instability and one for stability. The criteria depend only on the characteristics of the system. For a simple 2-DOF system, the present criteria yield the exact solutions. © 2006 Springer.