Exact stationary solutions of stochastically excited and dissipated gyroscopic systems

The Hamilton's equations of gyroscopic systems are derived.;It is pointed o ut that gyroscopic forces are derived from kinetic energy and/or potential energy, so they should be regarded as a part of Hamiltonian systems rather than externally generalized forces. A symplectic transformation matrix is p roposed to decouple the Hamilton's equations of linear gyroscopic systems. It is shown that the exact stationary solution of a stochastically excited and dissipated gyroscopic system is not affected by the gyroscopic forces w hen the gyroscopic system as a Hamiltonian system is non-integrable. When t he gyroscopic system is integrable, the stationary probability density and the statistics for various generalized coordinates vary with the gyroscopic forces while the mean total energy of the system is unchanged. A stochasti cally excited and dissipated gyropendulum is studied in detail to demonstra te the inferences. (C) 2000 Elsevier Science Ltd. All rights reserved.