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Analysis of motion for a rolling disc on the flat surface


International Robotics & Automation Journal
Ryspek Usubamatov
Kyrgyz State Technical University

Abstract

Background: Recent investigations in gyroscopic effects have demonstrated that their origin has more complex nature that represented in known publications. Actually, on a gyroscope are acting simultaneously and interdependently eight inertial torques around two axes. This torques is generated by the centrifugal, common inertial and Coriolis forces as well as the change in the angular momentum of the masses of the spinning rotor. The action of these forces manifests in the form of the inertial resistance and precession torques of gyroscopic devices. New mathematical models for the inertial torques acting on the spinning rotor demonstrate fundamentally different approaches and results of solving the problems of gyroscopic devices.The tendency in contemporary engineering is expressed by the increasing of a velocity of rotating objectslike turbines, rotors, discs and othersthat lead to the proportional increase of the magnitudes of inertial forces forming their motions. This work considers a typical example for computing of the inertial torques acting on the free rolling disc, which can be a bicycle wheel, rims, hoops, discs, and similar designs that express the gyroscopiceffects. 

Keywords

gyroscope theory, torques, motions, forces, mass of a disc, gravity acceleration, index for axis, radius of a disc, load torque, coefficient of correction, angular velocity of a disc, gyroscopic effects, disc produces, coriolis forces,

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