Theory of a gyroscopic pendulum
Abstract
A kinematic interpretation is given for the precession equations of a gyroscopic pendulum (GP) relative to a Darboux trihedron and for the precession equations of a GP relative to a geographical trihedron. Linear differential equations are obtained for the behavior of a GP in the case of finite angles of deviation of the rotor axis from the vertical for arbitrary motion of the point of its suspension on the earth's surface. These equations have the structure of the kinematic equations of spherical motion of a rigid body in RodriguesHamilton parameters. The Liapunov stability of the solutions of GP equations in finite Euler angles and in RodriguesHamilton parameters is demonstrated.
 Publication:

Prikladnaia Matematika i Mekhanika
 Pub Date:
 December 1980
 Bibcode:
 1980PriMM..44..986C
 Keywords:

 Body Kinematics;
 Equations Of Motion;
 Gyroscopic Pendulums;
 Gyroscopic Stability;
 Angular Velocity;
 Hamiltonian Functions;
 Kinematic Equations;
 Liapunov Functions;
 Vertical Motion;
 Instrumentation and Photography