written by Wolfgang Christian
The Gyroscope example computes and displays the dynamics of gyroscope under the influence of a gravitational torque acting on the center of mass. The gyroscope is supported at one end and given an initial angular velocity component about its axis of symmetry and a component perpendicular to its axis of symmetry. The numerical solution shows the motion for all initial conditions including zero initial angular momentum. The model is designed to show the cycloidal motion (precession and nutation) of the gyroscope axle when the initial angular velocity is large. Users can very the position and radius of the spinning mass as well as the initial angle and can display the angular momentum, angular velocity, and torque vectors. A second window shows the elevation angle of the axle and the angular momentum vector.
Units are chosen such that the total mass M and the acceleration of gravity g are one. The rotor is an ellipsoid with a uniform mass distribution and with major axes 2*R and minor axis R/5. The ellipsoid's moment of inertia through the center of mass is 4MR2/5 about the major axes and 26MR2/125 about the minor axis.
The Gyroscope model is a supplemental simulation for the article "It Has to Go Down a Little, in Order to Go Around" by Svilen Kostov and Daniel Hammer in The Physics Teacher 49(4), 216-219 (2011) and has been approved by the authors and The Physics Teacher editor. The model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_csm_ch17_Gyroscope.jar file will run the program if Java is installed.
Please note that this resource requires at least version 1.5 of Java.
AAAS Benchmark Alignments (2008 Version)
4. The Physical Setting
4E. Energy Transformations
AAAS Benchmark Alignments (1993 Version)
4. THE PHYSICAL SETTING
E. Energy Transformations
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Is Based On Easy Java Simulations Modeling and Authoring Tool
The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Gyroscope Model.relation by Wolfgang Christian
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