Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium

Акуленко, Л. Д.; Leshchenko, Dmytro; Rachinskaya, Alla

doi:10.3103/s0025654408020027

Cited by 17 publications

(8 citation statements)

References 8 publications

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“…e moments of inertia I i , i � 1, 2, 3 are assumed as arbitrary constants that satisfy the above condition, and λ 3 is estimated by substituting (7) into the second equation from (4). is problem has wide applications in satellite motions which assumed moments of inertia according to the above relations [16][17][18]. A numerical example is given to show the stability conditions for a special case.…”

Section: Discussionmentioning

confidence: 99%

The Stability Conditions for a Heavy Solid Motion

Ismail

2020

Mathematical Problems in Engineering

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In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

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Section: Discussionmentioning

confidence: 99%

The Stability Conditions for a Heavy Solid Motion

Ismail

2020

Mathematical Problems in Engineering

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“…New analytical and simulation outcomes for CBFTs along the minor, middle, or major axes are presented. The rapid rotational motions of unbalanced asymmetric satellites around their center of mass under the influence of both gravitational and drag torques are examined in 4 . It is concluded that the satellites’ kinetic energy and angular momentum decrease, in which they are identified in the presence of Quasi stationary motion phases.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

Amer,

El-Kafly,

Elneklawy

et al. 2024

Sci Rep

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This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.

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“…In the last few decades, many researchers have focused their work on studying the RB's motion when the applied external torques have various types. [1][2][3][4][5][6][7][8][9][10] The main factor of this progress is due to its broad range of uses in diverse fields, including satellites, spacecraft, and the like. An investigation of an asymmetrical satellite's motion under the action of pressure forces and resistive moments is presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…More contributions to this problem are discussed in Ref. 4 when the satellite is subjected to both drag and gravitational force. The authors considered that the drag torque is linearly related to the satellite’s angular velocity.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of an acted asymmetric rigid body by a gyrostatic moment and a constant body-fixed torque

Amer

Abady

Farag

2023

Journal of Low Frequency Noise, Vibration and Active Control

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This work focuses on the dynamical rotatory motion of an asymmetric rigid body (RB) subjected to a constant body-fixed torque and a vector of a gyrostatic moment (GM). The motion is considered in the absence of the first two components of the GM. The novelty of the current work is the conversion of the stability analysis of this body from a two dimensional phase plane to three ones phase space. Specifically, two scenarios of stationary torques are considered, the first one is directed on the minor or major axis, while the latter is presumed to act on the middle axis. Therefore, three dimensional phase space routes are generated. In both scenarios some novel analytical and simulation outcomes are provided regarding equilibrium manifolds, periodic solutions or non-periodic ones, separator surfaces, as well as the extreme periodic solutions. The significance of this work is due to its great applications, especially those that use the gyro’s theory.

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Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium

Cited by 17 publications

References 8 publications

The Stability Conditions for a Heavy Solid Motion

The Stability Conditions for a Heavy Solid Motion

Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

Stability analysis of an acted asymmetric rigid body by a gyrostatic moment and a constant body-fixed torque

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