DYNAMICAL CONTROL OF STABILITY FOR BIRKHOFFIAN SYSTEM

A dynamical control of the stability of equilibrium for the Birkhoffian system and generalized Birkhoffian system are studied. First, the equilibrium of motion and the equations of equilibrium of the systems are established. Secondly, the dynamical control of the stability of equilibrium for the Birkhoffian system where the Birkhoffian contain control parameters is investigated. The control parameters are chosen such that the Birkhoffian B becomes a definite function and its derivative of time \dot B is opposite sign. Thirdly, the dynamical control of the stability of equilibrium for Birkhoffian system where control parameters are contained in the Birkhoffian or in the additional terms is explored. Finally, some examples are given to illustrate the application of the results.