Attitude stability of a rigid body placed at an equilibrium point in the restricted problem of three bodies

1974 ◽  
Vol 10 (1) ◽  
pp. 17-33 ◽  
Author(s):  
W. J. Robinson
Keyword(s):  
Rigid Body ◽  
Equilibrium Point ◽  
Restricted Problem ◽  
Attitude Stability

Chaos in a restricted problem of rotation of a rigid body with a fixed point

2008 ◽  
Vol 13 (3) ◽  
pp. 221-233 ◽  
Author(s):  
A. V. Borisov ◽  
A. A. Kilin ◽  
I. S. Mamaev
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Restricted Problem

Displacement of the Lagrange Equilibrium Points in the Restricted Three Body Problem With Rigid Body Satellite

1978 ◽  
Vol 41 ◽  
pp. 305-314
Author(s):  
W.J. Robinson
Keyword(s):  
Rigid Body ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractIn the restricted problem of three point masses, the positions of the equilibrium points are well known and are tabulated. When the satellite is a rigid body, these values no longer correspond to the equilibrium points. This paper seeks to determine the magnitudes of the discrepancies.

scholarly journals Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Awadhesh Kumar Poddar ◽  
Divyanshi Sharma
Keyword(s):  
Perturbation Theory ◽  
Rigid Body ◽  
Coordinate System ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
General Perturbation ◽  
Triaxial Rigid Body ◽  
Three Dimensional Coordinate

AbstractIn this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

scholarly journals Multifarious Chaotic Attractors and Its Control in Rigid Body Attitude Dynamical System

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yang Wang ◽  
Zhen Wang ◽  
Dezhi Kong ◽  
Lingyun Kong ◽  
Yukun Qiao
Keyword(s):  
Rigid Body ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Euler Angle ◽  
Chaotic Attractors ◽  
Attitude Motion ◽  
Control Law ◽  
Relay Control ◽  
Body Attitude ◽  
The Stability

The Euler dynamical equation which describes the attitude motion of a rigid body will exhibit very complex dynamic behaviors under the action of different external torques. Many special types of new chaotic attractors are presented, including hidden attractors, double-body-double-core chaotic attractors, and single-body-three-core-tree-wing chaotic attractors. The position of equilibrium points in several typical cases of the Euler dynamic equation is solved, and the stability of linearized equation at each equilibrium point and its influence on the formation of the chaotic attractor are analyzed. An improved nonlinear relay control law based on Euler angle feedback is developed to stabilize a new chaotic spacecraft attitude motion to an appointed equilibrium point or a periodic orbit.

scholarly journals Chaos in a restricted problem of rotation of a rigid body with a fixed point

2005 ◽  
pp. 191-207
Author(s):  
A. V. Borisov ◽  
◽  
A. A. Kilin ◽  
I. S. Mamaev ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Restricted Problem

Attitude Stability and Control of the System Coupled with Main Rigid Body, Elastomer and Tip Rigid Body

2012 ◽  
Vol 588-589 ◽  
pp. 256-259
Author(s):  
Jian Guo Xu ◽  
Liang Hui Qu
Keyword(s):  
Rigid Body ◽  
Large Scale ◽  
System Analysis ◽  
Control Law ◽  
Controlled System ◽  
Attitude Stability ◽  
Infinite Dimensional ◽  
Stability And Control ◽  
And Control ◽  
Modern Mathematics

The dynamic model of a class of the system coupled with main rigid body, elastomer and tip rigid body is established. The control law of the system is given, and the attitude stability of the complex controlled system is studied in infinite dimensional functional spaces by means of the modern mathematics and large scale system analysis.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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