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The corrected mathematical models for the top motion


International Robotics & Automation Journal
Ryspek Usubamatov,1 Sarken Kapayeva2

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Abstract

The mathematical models for the top motions in known publications contain the incorrect expression of the centrifugal torque and do not consider the action of the Coriolis torque generated by the center mass. In reality, the two centrifugal torques, two torques of Coriolis forces, and two changes in the angular momentums formulate the dependency of the angular velocities of the top motions about two axes. The corrected expression of the centrifugal torque and the Coriolis torque generated by the center mass changed the mathematical models for the top motion and its self-stabilization. The new analytical approach for the spinning top motions with the action of all external and inertial torques gives an accurate solution and describes its physics. The derived mathematical models for the spinning top motions and solution represent a good example of the educational process of engineering mechanics.

Keywords

physics of gyroscopic effects, inertial torque, top motions

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