修正了顶部运动的数学模型

R. Usubamatov, S. Kapayeva
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引用次数: 0

摘要

已知文献中关于陀螺运动的数学模型包含了离心力矩的不正确表达式,并且没有考虑质心产生的科里奥利力矩的作用。实际上,两个离心力矩,科里奥利力的两个力矩,角动量的两个变化构成了顶部运动角速度在两个轴上的依赖关系。离心力矩和质心产生的科里奥利力矩的修正表达式改变了陀螺运动及其自稳定的数学模型。对于所有外力矩和惯性力矩作用下的旋转陀螺运动,给出了精确的解析解,并描述了其物理性质。推导出的旋顶运动数学模型及其解是工程力学教学过程的一个很好的例子。
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The corrected mathematical models for the top motion
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.
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