A mathematical model for motions of gyroscope suspended from flexible cord

Usubamatov, Ryspek

doi:10.1080/23311916.2016.1245901

Cited by 18 publications

(21 citation statements)

References 12 publications

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“…That giving rise to the following -0. 007560157< 0.002882717 (16) The right component of equation (16) is bigger than the left one. It means the inertial torques acting on the top turn up to vertical with the spiral motion of the top on the surface.…”

Section: Self-stabilizationmentioning

confidence: 95%

“…The parameters defined above allow for the formulation of a mathematical model for a top's motion around axes ox and oy in Euler's form. The torques acting on the top are similar to the torques acting on the gyroscope suspended from a flexible cord [16]. Both models consider the motion of the spinning disc with one-side support.…”

Section: Figure 1: Forces Acting On a Spinning Topmentioning

confidence: 99%

“…The methodology towards a solution for equation (1) -(2) by using the ratio of the precession velocities of a top around axes (equation (3)) is represented in [16]. Substituting equations (3) and (4) and equations of inertial torques [15] into equations (1) and (2) and simplification yield the following equations of the top's motion around axis ox:…”

Section: Figure 1: Forces Acting On a Spinning Topmentioning

confidence: 99%

“…The motion of a spinning top that inclined to a horizontal flat surface is complex. The equation of motion is formulated by the action of several forces and torques on the top that is as follows: the external torque generated by action of the weight of an inclined top; the torque generated by the centrifugal force of the rotating top's centremass around axis oy; the external torque generated by the frictional force acting on the top's leg and around its axis.Other acting inertial torques is generated by the rotating masses mentioned above and represented in several publications [15,16]. All forces and torques acting on the top are demonstrated in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…Recent investigations into the physical principles of gyroscope motions demonstrate the system of interrelated inertial forces acting upon a spinning disc. Gyroscope effects generated by the action of the centrifugal, common inertial, and Coriolis forces, and the change in the angular momentum of the spinning disc [15][16][17]. The action of these forces is manifested by the resistance and precession torques which formulate the motions of the gyroscopic devices [18,19].…”

Section: Introductionmentioning

confidence: 99%

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A Mathematical Model for Top Motions

2019

ATCP

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The topic of the top motions is not new but the known publications represent wrong mathematical models for its gyroscopic effects. Recent investigations have demonstrated the physics of gyroscopic effects is more complex. On any spinning objects are acting the system of interrelated internal torques generated by their rotating mass elements and center mass. The inertial torque is produced by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum. These inertial torqueses represent the fundamental principle of gyroscope theory. The new inertial torques enables deriving mathematical models for the motions of any rotating objects that were impossible for a long time. The aim of this work is to represent mathematical models for the motions of the well-balanced top on the flat horizontal surface. This work describes the physics of the top motions and closes the problem of many years of discussion. The new analytical approach for the top’s motions definitely responds to the practical results and represents a good example of the educational process.

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Section: Self-stabilizationmentioning

confidence: 95%

Section: Figure 1: Forces Acting On a Spinning Topmentioning

confidence: 99%

Section: Figure 1: Forces Acting On a Spinning Topmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%