Short Notes on the Rotatory Motion of a Rigid Body
TS Amer1* and WS Amer2
1Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
2Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt
*Corresponding Author: TS Amer, Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.
September 23, 2022; Published: September 28, 2022
In this short study, light is shed on the rotatory motion of a rigid body about a fixed point under the action of different external fields and moments. These fields can be considered as gravitational, Newtonian, and electromagnetic, while the moments are represented by gyrostatic, perturbing, and restoring moments. Some of the perturbation methods are viewed to show how much they are involved in the solutions to this problem.
Keywords: Rigid Body; Rotatory Motion; Equations of Motion (EOM)
- H M Yehia. “Rigid body dynamics: A Lagrangian approach”. Birkhäuser, Springer Nature Switzerland AG (2022).
- Arkhangel'skii Iu A. “On the algebraic integrals in the problem of motion of a rigid body in a newtonian field of force”. Journal of Applied Mathematics and Mechanics1 (1963): 247-254.
- H M Yehia. “New integrable cases in the dynamics of rigid bodies”. Mechanics Research Communications 13 (1986): 169-172 (1986).
- H M Yehia and A A Elmandouh. “A new conditional integrable case in the dynamics of a rigid body-gyrostat”. Mechanics Research Communications 78 (2016): 25-27.
- T S Amer and W S Amer. “The substantial condition for the fourth first integral of the rigid body problem”. Mathematics and Mechanics of Solids8 (2018): 1237-1246.
- N N Bogoliubov and YA Mitropolsky. “Asymptotic methods in the theory of non-linear oscillations”. Gordon and Breach, New York (1961).
- AH Nayfeh. “Perturbations methods”. WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim (2004).
- Arkhangel'skii Iu A. “On the motion about a fixed point of a fast spinning heavy solid”. PMM5 (1963): 864-877.
- Arkhangel'skii Iu A. “Construction of periodic solutions for the Euler-Poisson equations by means of power series expansion containing a small parameter”. Colloquia Mathematica Societatis Janos Bolyai, Keszthely (Hungary), (1975): 27-50.
- F A El-Barki and A I Ismail. “Limiting case for the motion of a rigid body about a fixed point in the Newtonian force field”. ZAMM11 (1995): 821-829.
- A I Ismail and T S Amer. “The fast spinning motion of a rigid body in the presence of a gyrostatic momentum”. Acta Mechanica 154 (2002): 31-46.
- T S Amer. “Motion of a rigid body analogous to the case of Euler and Poinsot”. Analysis 24 (2004): 305-315.
- T S Amer and W S Amer. “The rotational motion of a symmetric rigid body similar to Kovalevskaya's case”. Iranian Journal of Science and Technology, Transactions A: Science3 (2018): 1427-1438.
- J H He., et al. “Modelling of the rotational motion of 6-DOF rigid body according to the Bobylev-Steklov conditions”. Results in Physics 35 (2022): 105391.
- A M Farag., et al. “The periodic solutions of a symmetric charged gyrostat for a slightly relocated center of mass”. Alexandria Engineering Journal 61 (2022): 7155-7170.
- A I Ismail. “Treating the Solid Pendulum Motion by the Large Parameter Procedure”. International Journal of Aerospace Engineering (2020).
- A I Ismail. “New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency”. Advances in Astronomy (2020).
- A I Ismail. “New Vertically Planed pendulum motion”. Advances in Astronomy (2020).
- A I Ismail. “On the application of Krylov-Bogoliubov-Mitropolski technique for treating the motion about a fixed point of a fast spinning heavy solid”. ZFW 20 (1996): 205-208.
- T S Amer., et al. “Application of the Krylov-Bogoliubov-Mitropolski technique for a rotating heavy solid under the influence of a gyrostatic moment”. Journal of Aerospace Engineering3 (2012): 421-430.
- T S Amer and IM Abady. “On the application of KBM method for the 3-D motion of asymmetric rigid body”. Nonlinear Dynamics 89 (2017): 1591-1609.
- T S Amer., et al. “The dynamical motion of a rigid body for the case of ellipsoid inertia close to ellipsoid of rotation”. Mechanics Research Communications 108 (2020): 103583.
- L D Akulenko., et al. “Perturbed motions of a rigid body that are close to regular precession”. Izv. Akad. Nauk SSSR. MTT 21.5 (1986): 3-10.
- L D Akulenko., et al. “Evolution of rotations of a rigid body under the action of restoring and control moments”. Journal of Computer and System Sciences 5 (2002): 868-874.
- T S Amer., et al. “On the motion of a gyro in the presence of a Newtonian force field and applied moments”. Mathematics and Mechanics of Solids9 (2018): 1263-1273.
- A I Ismail., et al. “Electromagnetic gyroscopic motion”. Journal of Applied Mathematics (2012): 1-14.
- T S Amer. “On the rotational motion of a gyrostat about a fixed point with mass distribution”. Nonlinear Dynamics 54 (2008): 189-198.
- T S Amer. “The rotational motion of the electromagnetic symmetric rigid body”. Applied Mathematics and Information Sciences 4 (2016): 1453-1464.
- W S Amer. “The dynamical motion of a gyroscope subjected to applied moments”. Results in Physics 12 (2019): 1429-1435.