On the Spinning Motion of a Disc under the Influence a Gyrostatic Moment

Bek, M. A.; Amer, T. S.; Gamiel, Yasser

doi:10.1007/978-3-030-77314-4_1

Cited by 3 publications

(3 citation statements)

References 18 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on Ref. 53, we note that the conditions (18) do not affect the required general solutions. The generated system (15) gives the analytic periodic solutions of the period T 0 =n ¼ 2π as…”

Section: Constructing the Analytic Periodic Solutionsmentioning

confidence: 89%

A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

Ismail

Abdulaziz

2022

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

A rotary motion is studied, which is used as a paradigm in both mathematics and dynamics. In this motion, the body moves around its axis. Important examples of this motion are the earth, wheels for cars or bicycles, cooling fans, airplanes, radars, and motion of the discs. In this article, we consider one of these motions such as the slow rotational motion of a disc of high natural frequency around a fixed point different from its center of mass. Suppose a constant gyrostatic couple acts on the body about the axis of symmetry. Let us consider the axis of symmetry coincide with one of the main axes of inertia. The controlled nonlinear independent system of equations of motion is obtained in the form of six nonlinear differential equations in the presence of three independent first integrals. This system is reduced to an alternative independent quasi-linear system consisting of two differential equations with only one integral. At first, when the body rotates slowly with a small angular speed about the axis of the symmetry, we achieve a large parameter for the motion which is proportional to the inverse of the angular velocity component. Then, we use the large parameter technique to obtain approximate and high-frequency analytic solutions for this motion. This technique enables us to introduce new conditions of the motion, save a lot of energy required to move the disc, and obtain new approximated solutions in a new domain of the disc parameters. We present a digital example of the problem to clarify the inferences of the motion depending on the parameters of the body. On the other hand, we use the Runge–Kutta algorithmic method to obtain the numerical solutions corresponding to the approximate solutions of the considered independent system. We investigate the inaccuracies and errors of analytic and numerical solutions by comparing them. This problem offers many applications in gyroscope dynamics, industrial engineering, astrophysics, navigation, satellites, and space engineering.

show abstract

Section: Constructing the Analytic Periodic Solutionsmentioning

confidence: 89%

A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

Ismail

Abdulaziz

2022

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

“…It is significant to note that the obtained solutions (40) do not involve any singular points owing to the usage of Amer’s frequency, unlike earlier works such as 22 – 24 when equals or their multiple inverses. The gained solutions are applicable for all rational values of and are considered generalizations of 33 and 35 .…”

Section: Constructing the Periodic Solutionsmentioning

confidence: 99%

“…These singularities have been separately treated according to the values of the body’s natural frequency in 23 , 34 . The impact of one component of the GMV on the disc’s motion is investigated in 35 . The importance of this component lies in the fact that the solutions that have been reached do not contain any singular points.…”

Section: Introductionmentioning

confidence: 99%

Studying the influence of external moment and force on a disc’s motion

Amer

Elkafly

2022

Sci Rep

View full text Add to dashboard Cite

In this work, the influence of a gyrostatic moment vector (GMV) and the Newtonian field (NF) on the rotatory motion of a restricted rigid body (RB) according to disc case around a fixed point is examined. The basic equation of the body motion is used to get the regulating motion’s system as well as the three available independent first integrals. The system’s six equations and these integrals were reduced to two equations of a quasi-linear two-degrees-of-freedom autonomous system and one first integral. The disc has been presumed to be quickly rotating around one of the ellipsoid of inertia's main axis. Poincaré’s method of small parameter (PMSP) is applied to acquire the periodic solutions of the controlling system of the body’s motion. Euler's angles are utilized to characterize the body’s configuration at any instant in which it is graphed, as well as the obtained solutions to explore the good action of the body’s parameters on its motion. The phase plane graphs of these solutions are presented to examine their stabilities. The relevance of this work may be traced to its wide range of applications in fields as diverse as physics, engineering, and life sciences, including assembly and machine design.

show abstract

Modelling of the rotational motion of 6-DOF rigid body according to the Bobylev-Steklov conditions

Amer

Elkafly

et al. 2022

Results in Physics

View full text Add to dashboard Cite

On the Spinning Motion of a Disc under the Influence a Gyrostatic Moment

Cited by 3 publications

References 18 publications

A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

Studying the influence of external moment and force on a disc’s motion

Modelling of the rotational motion of 6-DOF rigid body according to the Bobylev-Steklov conditions

Contact Info

Product

Resources

About