Dynamics of a rigid body on an inertial elastic foundation

The problems of construction of high-speed centrifuges, with rotational velocities 120 000 - 200 000 revolutions per minute, required the development of more sophisticated mechanical models. As such a model it is chosen a rigid body on an elastic foundation. The parameters of the rotor and of the elastic foundation do not allow to consider the elastic foundation as inertialess. There was proposed (1995) a method [1, 2], allowing to reduce the problem to the solution of a relatively simple integro-differential equation.
  1. Zhilin P.A., Tovstik T.P. Rotation of a rigid body based on an inertial rod // Mechanics and Control. Proc. of St. Petersburg State Technical University. 1995. N 458. P.78-83. (In Russian).
  2. Ivanova E.A., Zhilin P.A. Non-stationary regime of the motion of a rigid body on an elastic plate // Proc. of XXIX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg. 2002. P. 357-363.