Mathematical model for gyroscope effects

Usubamatov, Ryspek

doi:10.1063/1.4915651

Cited by 11 publications

(13 citation statements)

References 5 publications

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“…The simultaneous action of this group of forces and their interrelations has not been described in the physics of gyroscope effects. Based on new fundamental approaches the gyroscope effects are represented by new mathematical model [14][15][16][17][18]. This model is well-matched with practical results that conducted on the Super Precision Gyroscope model "Brightfusion Ltd".…”

Section: Introductionmentioning

confidence: 89%

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Properties of Gyroscope Motion About One Axis

Usubamatov

2014

Second International Conference on Advances in Mechanical, Aeronautical and Production Techniques - MAPT 2014

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The known gyroscope theory based on principle of the rate change in the angular momentum of a spinning rotor. Practice demonstrates this mathematical model cannot describe other gyroscope effects and shows that there are other unsolved problems, which is spawned steady myth of the gyroscope mystery. These phenomena attract new researchers to solve gyroscope problems. The nature of gyroscope effects is more complex than represented in publications and known mathematical models do not match the actual motions and forces of the gyroscope effects. Latest studies of forces that involved in motions of a gyroscope demonstrate that there are four dynamical components, which act simultaneously and interrelated. The gyroscope with the external torque applied is experienced the resistance torque generated by the centrifugal and Coriolis forces and the precession torque generated by the inertial forces and the rate change of the angular momentum of the spinning rotor. These four dynamical components is represented the fundamental principles of gyroscope theory. Interrelation of this torques demonstrates the new unknown effects of the gyroscope. In case of the blocking the action of the precession torques resistance torques are deactivated. The mathematical model of forces acting in the gyroscope practically tested and the results validated the theoretical approach.

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Section: Introductionmentioning

confidence: 89%

“…and transforming enable to represent the integral form of Eq. (15) is as follows: of x into Eq (17). and transforming yield the following equation: speed of the gyroscope rotor ω = 10,000 rpm and inclination of the gyroscope axis on angle γ = 60 0 into Eq.…”

mentioning

confidence: 99%

Properties of Gyroscope Motion About One Axis

Usubamatov

2014

Second International Conference on Advances in Mechanical, Aeronautical and Production Techniques - MAPT 2014

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“…The new mathematical models for gyroscope motions will consider the simultaneous and interdependent actions of internal torques ( Table 1). The external load torque generates eight internal resistance and precession torques acting around two axes and reveals new gyroscope properties [21]. The interdependent action of internal torques is used to model the behavior of different gyroscopic devices, including the simplest top.…”

Section: Methodsmentioning

confidence: 99%

“…Recent investigations into the physical principles of gyroscope motions demonstrate four classical inertial forces acting upon a spinning rotor to generate the gyroscope effects. Research shows that centrifugal, common inertial, and Coriolis forces, in addition to change in the angular momentum of spinning rotors, are the basis for all gyroscope effects and properties [21][22][23][24]. Applied to the gyroscope, an external torque generates several torques based on the action of the aforementioned forces.…”

Section: Introductionmentioning

confidence: 99%

“…All torques are interrelated and occur simultaneously. New mathematical models for acting torques accurately describe the physics of gyroscope effects and are validated by tests [21]. Table 1 represents four different torques generated by the inertial forces of the mass elements and centermass of the spinning rotor under the action of the external torque that was applied to the gyroscope.…”

Section: Introductionmentioning

confidence: 99%

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A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

Usubamatov

Omorova

2018

Mathematical Problems in Engineering

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The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.

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Inertial Forces and Torques Acting on Simple Spinning Objects

Usubamatov

2022

Theory of Gyroscopic Effects for Rotating Objects

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Mathematical model for gyroscope effects

Cited by 11 publications

References 5 publications

Properties of Gyroscope Motion About One Axis

Properties of Gyroscope Motion About One Axis

A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

Inertial Forces and Torques Acting on Simple Spinning Objects

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