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

Abstract

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.

Advanced investigations of a restricted gyrostatic motion

“…Numerous researchers were interested in the dynamics of a six-degrees-of-freedom (DOF) rigid body (RB) with a single fixed-point, for example. [1][2][3][4][5][6][7][8][9][10][11][12][13] The reason is due to its several applications in particle life, like airplanes, submarine vehicles, spacecraft, and other applications that depend on the gyroscopic theory. It is considered in, 1 the problem of the motion of an asymmetric solid body rotating around a fixed under the influence of a uniform field of gravitational attraction.…”

“…Based on the EOM and first integrals, an autonomous system of 2DOF is obtained in Ref. 9–13 with one integral. The authors considered the action of a gyrostatic moment (GM) and the Newtonian field of force (NFF) on the body’s motion when the values of the main axes have different values, 9 for the situations of Euler-Poinsot, 10 Kovalevskaya, 11,12 and the disc’s case.…”

Sufficiently small rotations of Lagrange’s gyro

“…When the movement of RB is taken into account while being impacted by a gravitational field, a Newtonian field (NF), an electromagnetic field (EMF), and the existence of a gyro torque (GT), the MSPM is employed in [10][11][12][13][14][15][16][17][18][19][20][21][22] to find its AS in 10,11 under the action of a uniform gravity field, while 12 looks into how the NF affects on the RB motion. It should be mentioned that when the frequency of the system had integer values or their multiple inverses, the resulting solutions consisted of discrete singular points.…”

“…The acquired results are regarded as a generalization of those found in 18 and. 19 See [20][21][22] for further details on how the strategy of this method might be used to address different SB issues.…”

“…[26][27][28][29][30][31] This motion has been studied in three different cases: when the body was impacted by a uniform gravity field, 26,27 an NF, 28,29 and the action of a GT. 22,23 The effect of perturbing moments on a body's motion has been taken into account. The guiding EOM is constructed using the basic equation of the RB angular momentum, where a tiny parameter was added by using some applied assumptions.…”