Stability of the uniform rotations of a gyrostat about the main vertical axis on an absolutely smooth horizontal plane
Abstract
A Hamiltonian function is obtained which specifies canonic equations of motion for the case of a gyrostat rotating on an absolutely smooth horizontal plane. The equations permit particular solutions for the uniform rotations of a gyrostat about the main vertical axis coinciding with the axis of uniform rotations of the rotor. A reduced system with two degrees of freedom is then derived, and a Hamiltonian expansion in the neighborhood of the corresponding equilibrium point is obtained with an accuracy up to fourth-order terms. Sufficient conditions for the stability of uniform gyrostat rotations are obtained in terms of constraints on the coefficients of normal forms. For a graphic interpretation of results, particular cases are considered where all but two parameters are fixed.
- Publication:
-
Prikladnaia Matematika i Mekhanika
- Pub Date:
- February 1986
- Bibcode:
- 1986PriMM..50...73B
- Keywords:
-
- Flat Surfaces;
- Gyroscopic Stability;
- Rotary Gyroscopes;
- Rotary Stability;
- Canonical Forms;
- Equations Of Motion;
- Hamiltonian Functions;
- Rotors;
- Physics (General)