Linear orbital stability analysis of the pendulum-type motions of a Kovalevskaya top with a suspension point vibrating horizontally

International Conference of Young Scientists and Students "Topical Problems of Mechanical Engineering 2018"

Belichenko, M.V.^1

Moscow Aviation Institute, National Research University, Moscow, Russia^1

关键词: Autonomous systems;    Heavy rigid body;    High frequency HF;    Horizontal vibration;    Kovalevskaya top;    Orbital stability;    Principal axis;    Vertical plane;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/489/1/012034/pdf
DOI  :  10.1088/1757-899X/489/1/012034

来源: IOP

【 摘 要 】

The motion of a heavy rigid body is considered, with a point (suspension point) performing high-frequency horizontal vibration. The center of mass of the body is on the principal axis of inertia for this point. Within the framework of an approximate autonomous system, pendulum-type motions of the body are studied, they occur in a vertical plane containing the axis of vibration or in a plane perpendicular to it. For a body with a mass geometry corresponding to S. V. Kovalevskaya case, a linear orbital stability analysis of these motions is performed.