On the motion of a gyro in the presence of a Newtonian force field and applied moments

Amer, T. S.; Abady, I. M.

doi:10.1177/1081286517716734

Cited by 27 publications

(23 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e advantage of this method is that the energy motion of the body is assumed to be sufficiently small instead of sufficiently large with other techniques [10][11][12]. Also, the obtained solutions treat a singular situation for the natural frequency which was excluded from previous works [13,14].…”

Section: Discussionmentioning

confidence: 99%

New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

Ismail

2020

Advances in Astronomy

View full text Add to dashboard Cite

In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω = 0.5 . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.

show abstract

Section: Discussionmentioning

confidence: 99%

New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

Ismail

2020

Advances in Astronomy

View full text Add to dashboard Cite

show abstract

“…The averaging method 7 , 11 has a wide spread in many scientific works to address the rotational motion of the RB problem, whether in the symmetric gravitational field 12 , 13 or the NF 14 , 15 or even in the presence of a gyrostatic moment and a magnetic field 16 – 18 . These works were explored when the applied operating perturbing moments along the primary axes of inertia are assumed to be constants.…”

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

“…This anomaly appeared in [2] and is specialized in various bodies classified according to the inertia. Using the Poincare small-parameter method [3], periodic solutions-with basic zero amplitudes-of the semilinear independent system were obtained in the form of power series expansions up to the third approximation containing assumed small parameters. In [4], Poincare's method that depends on a small parameter assumed to be inversely proportional to a high angular velocity component r o is studied.…”

Section: Introductionmentioning

confidence: 99%

Application of a Large-Parameter Technique for Solving a Singular Case of a Rigid Body

Ismail

2021

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this paper, the motion of a rigid body in a singular case of the natural frequency ( ω = 1 / 3 ) is considered. This case of singularity appears in the previous works due to the existence of the term ω 2 − 1 / 9 in the denominator of the obtained solutions. For this reason, we solve the problem from the beginning. We assume that the body rotates about its fixed point in a Newtonian force field and construct the equations of the motion for this case when ω = 1 / 3 . We use a new procedure for solving this problem from the beginning using a large parameter ε that depends on a sufficiently small angular velocity component r o . Applying this procedure, we derive the periodic solutions of the problem and investigate the geometric interpretation of motion. The obtained analytical solutions graphically are presented using programmed data. Using the fourth-order Runge-Kutta method, we find the numerical solutions for this case aimed at determining the errors between both obtained solutions.

show abstract

On the motion of a gyro in the presence of a Newtonian force field and applied moments

Cited by 27 publications

References 18 publications

New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

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

Application of a Large-Parameter Technique for Solving a Singular Case of a Rigid Body

Contact Info

Product

Resources

About