WIAS Preprint No. 883, (2003)

Stability of gyroscopic systems under small random excitations


  • Khasminskii, Rafail
  • Milstein, Grigori N.

2010 Mathematics Subject Classification

  • 60H10 93E15


  • Stochastic stability, Lyapunov exponents, moment Lyapunov exponents, oscillators with small random excitations, gyroscopic forces, stochastic averaging principle




Gyroscopic systems with two degrees of freedom under small random perturbations are investigated by use of the stochastic averaging principle. It is proved that the principal term of the Lyapunov exponent for the original system coincides with the Lyapunov exponent for the averaged system. An explicit formula for the averaged Lyapunov exponent is derived. The averaged moment Lyapunov exponent is considered as well. An example is given in which an unstable gyroscopical system is stabilized by noise of the Sratonovich type.

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