The dynamical motion of a rigid body for the case of ellipsoid inertia close to ellipsoid of rotation

Amer, T. S.; Farag, A. M.; Amer, W. S.

doi:10.1016/j.mechrescom.2020.103583

Cited by 17 publications

(12 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) Time-reversible case: this case is characterized by the absence of gyroscopic forces, i.e., Ω � 0. is happens if a 1 � 0anda 2 � 0, e potential function (25) reduces to U � u(p) + a 3 v(p)sin ξ which is a Kowalevski-type potential. Furthermore, if we change ξ ⟶ 2ξ, the potential function takes the form U � u(p) + a 3 v(p)sin 2 ξ which is a Chaplygin-type potential.…”

Section: Applications To Rigid Body Dynamicsmentioning

confidence: 99%

“…(a) When setting a 1 � 0, the gyroscopic forces is characterized by Ω � a 2 Ω 0 (p), and the potential function (25) becomes U � u(p) + a 3 v(p)sin ξ. e potential function is a type of Kowalevskigyrostat type potential or Chaplygin-gyrostat type potential (if ξ ⟶ 2ξ ).…”

Section: Applications To Rigid Body Dynamicsmentioning

confidence: 99%

“…One of the significant issues in applications in assorted branches of science such as physics and astronomy is the problem of a rigid body and its extension to a gyrostat (see, e.g., [21][22][23]). So, it is a beneficial model for research from different points of view [24][25][26][27][28][29]. Consequently, the present work interested in analyzing the general motion of a rigid body about its fixed point that happens under the effect of a combination of potential (velocity-independent) forces and gyroscopic (velocity-dependent) forces.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quartic Integral in Rigid Body-Gyrostat Dynamics

Mnasri

Elmandouh

2020

Advances in Astronomy

View full text Add to dashboard Cite

In this work, we investigate the problem of constructing new integrable problems in the dynamics of the rigid body rotating about its fixed point as results of the effect of a combination of potential and gyroscopic forces possessing a common symmetry axis. We introduce two new integrable problems in a rigid body dynamics that generalize some integrable problems in this field, known by names of Chaplygin and Yehia–Elmandouh.

show abstract

Section: Applications To Rigid Body Dynamicsmentioning

confidence: 99%

Section: Applications To Rigid Body Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quartic Integral in Rigid Body-Gyrostat Dynamics

Mnasri

Elmandouh

2020

Advances in Astronomy

View full text Add to dashboard Cite

show abstract

“…The approximate solutions of the RB problem are gained in many literatures e.g. 5 – 17 , using various perturbation approaches such as the methods of the small parameter (MSP), averaging (MA), Krylov–Bogoliubov-Mitropolsky (MKBM), and others 36 , 37 . In 5 , these solutions are obtained using the MSP when the motion is considered in a gravitational field and are generalized in 6 , 7 to gain valid solutions at any value of the problem’s frequency when the Newtonian field and one of the third component of the GM are kept in mind.…”

Section: Introductionmentioning

confidence: 99%

Modeling a semi-optimal deceleration of a rigid body rotational motion in a resisting medium

El-Sabaa

Amer

Sallam

et al. 2022

Sci Rep

View full text Add to dashboard Cite

This paper studies the shortest time of slowing rotation of a free dynamically asymmetric rigid body (RB), analogous to Euler’s case. This body is influenced by a rotatory moment of a tiny control torque with closer coefficients but not equal, a gyrostatic moment (GM) due to the presence of three rotors, and in the presence of a modest slowing viscous friction torque. Therefore, this problem can be regarded as a semi-optimal one. The controlling optimal decelerating law for the rotation of the body is constructed. The trajectories that are quasi-stationary are examined. The obtained new results are displayed to identify the positive impact of the GM. The dimensionless form of the regulating system of motion is obtained. The functions of kinetic energy and angular momentum besides the square module are drawn for various values of the GM’s projections on the body’s principal axes of inertia. The effect of control torques on the body's motion is investigated in a case of small perturbation, and the achieved results are compared with the unperturbed one. For the case of a lack of GM, the comparison between our results and those of the prior ones reveals a high degree of consistency, in which the deviations between them are examined. As a result, these outcomes generalized those that were acquired in previous studies. The significance of this research stems from its practical applications, particularly in the applications of gyroscopic theory to maintain the stability and determine the orientation of aircraft and undersea vehicles.

show abstract

“…Amer et al (2018aAmer et al ( , 2018b used multiple scales (MS) technique to obtain the approximate solutions of the equations of motion and studied the stability of the governing system of motion. Besides, the fourth-order Runge-Kutta method is used to obtain the numerical solutions of the considered motion and compared with the analytical one to verify the rationality of the analytical results (Amer 2017;Amer et al 2020;2021).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and control of a flywheel energy storage rotor with rotational damping and nonsynchronous damping

Wang

Peng

Zhen

2021

Journal of Vibration and Control

View full text Add to dashboard Cite

Based on the principle of Lagrange mechanics, especially considering the effects of rotation damping and nonsynchronous damping, a radial 4-dimensional dynamic model of the flywheel bearing rotor system is proposed. Applying the Laplace eigenvalue method, the stability effects of rotational damping, nonsynchronous damping, and their coupling effects are investigated by means of root locus method. Under the control of the linear quadratic regulator, dynamical characteristics of the flywheel bearing rotor system with varied rotational damping and nonsynchronous damping are also studied. The results show that the rotation damping, nonsynchronous damping, and their coupling effects have vast and complex instability effects on high-speed flywheel bearing rotor system. However, there are three exceptions. The tiny proportional rotational damping, remaining below 12%, and the minuscule proportional co-nonsynchronous damping; the product of the nonsynchronous damping and the speed ratio below 5% both can enhance the stability of the system. Furthermore, in the situation that the counter-nonsynchronous damping is coupled with the large proportion of rotational damping, the stability of the system can also be boosted distinctly. On the other hand, the numerical experimental results show that the rotational damping and nonsynchronous damping have a beneficial effect on the flywheel system controlled by linear quadratic regulator. In addition, under the control of linear quadratic regulator, the transient dynamical behavior of the flywheel rotor system with rotational damping or co-nonsynchronous damping performed better than the flywheel rotor system with the coupled damping. The numerical simulations of the transient response of the flywheel rotor system under active control are consistent with some of the derived stability analysis results. The results about the stability analysis and the performance in vibration control give the suggestions for the instability control and fault detection of the system.

show abstract

The dynamical motion of a rigid body for the case of ellipsoid inertia close to ellipsoid of rotation

Cited by 17 publications

References 28 publications

Quartic Integral in Rigid Body-Gyrostat Dynamics

Quartic Integral in Rigid Body-Gyrostat Dynamics

Modeling a semi-optimal deceleration of a rigid body rotational motion in a resisting medium

Stability analysis and control of a flywheel energy storage rotor with rotational damping and nonsynchronous damping

Contact Info

Product

Resources

About