Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®

Russell, Kevin; Shen, Qiong; Sodhi, Raj S.

doi:10.1201/9780429506253

Cited by 13 publications

(15 citation statements)

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“…The centrifugal force of the eccentric mass generates the variable torque represented by the following equation [7]:…”

Section: Methodsmentioning

confidence: 99%

“…where all parameters are as specified above. Solving (6), (7), and (8) yields the maximum and minimum angular precessions and which allow for defining the nutation amplitudes around axes and , respectively. Changes in the angular velocities of precessions around two axes make it possible to depict the trajectory of a top's centermass nutation.…”

Section: Methodsmentioning

confidence: 99%

“…Gyroscope effects are used in numerous gyroscopic devices in aerospace engineering, as well as on ships and other industries [4,5]. The most basic textbooks of classical mechanics have chapters on the gyroscope theory [6,7] and consider motions with vibrations analysis [8]. Numerous and valuable publications have dedicated themselves to gyroscope effects and their applications in engineering [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…The centrifugal force of the eccentric mass generates the variable torque represented by the following equation [7]:…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Usubamatov

Omorova

2018

Mathematical Problems in Engineering

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“…For the solution, equation (6) is transformed, simplified and variables separated that yield the following differential equation: (8) Substituting initial data into equation (8) brings the following expression:…”

Section: 1125×10 -5mentioning

confidence: 99%

“…Gyroscopic effects are used in gyroscopic devices in aerospace engineering, as well as on ships and other industries [3,4]. The importance of the action of gyroscopic inertial forces on rotating objects is obvious and all textbooks of classical mechanics have chapters on the gyroscope theory [5][6][7][8]. Numerous and valuable publications have dedicated to gyroscopic effects and their applications in engineering [9,10].…”

Section: Introductionmentioning

confidence: 99%

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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Acceleration Analysis of Rotating Objects

Usubamatov

2022

Theory of Gyroscopic Effects for Rotating Objects

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Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®

Cited by 13 publications

References 0 publications

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

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

A Mathematical Model for Top Motions

Acceleration Analysis of Rotating Objects

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