scholarly journals Asteroid triple-system 2001 SN263: surface characteristics and dynamical environment

2020 ◽  
Vol 492 (3) ◽  
pp. 4437-4455 ◽  
Author(s):  
O C Winter ◽  
G Valvano ◽  
T S Moura ◽  
G Borderes-Motta ◽  
A Amarante ◽  
...  
Keyword(s):  
Interplanetary Space ◽  
Equilibrium Points ◽  
Surface Characteristics ◽  
Space Mission ◽  
Stable Region ◽  
Uniform Density ◽  
Triple Systems ◽  
Spherical Cloud ◽  
Zero Velocity Curves ◽  
Near Earth Asteroids

ABSTRACT The (153591) 2001 SN263 asteroid system, a target of the first Brazilian interplanetary space mission, is one of the known three triple systems within the population of near-Earth asteroids. One of the mission objectives is to collect data about the formation of this system. The analysis of these data will help in the investigation of the physical and dynamical structures of the components (Alpha, Beta, and Gamma) of this system, in order to find vestiges related to its origin. In this work, we assume the irregular shape of the 2001 SN263 system components as uniform-density polyhedra and computationally investigate the gravitational field generated by these bodies. The goal is to explore the dynamical characteristics of the surface and environment around each component. Then, taking into account the rotational speed, we analyse their topographic features through the quantities geometric altitude, tilt, geopotential, slope, and surface accelerations among others. Additionally, the investigation of the environment around the bodies made it possible to construct zero-velocity curves, which delimit the location of equilibrium points. The Alpha component has a peculiar number of 12 equilibrium points, all of them located very close to its surface. In the cases of Beta and Gamma, we found four equilibrium points not so close to their surfaces. Then, performing numerical experiments around their equilibrium points, we identified the location and size of just one stable region, which is associated with an equilibrium point around Beta. Finally, we integrated a spherical cloud of particles around Alpha and identified the location on the surface of Alpha where the particles have fallen.

On the Challenges of Anesthesia and Surgery during Interplanetary Spaceflight

2021 ◽  
Author(s):  
Matthieu Komorowski ◽  
Séamus Thierry ◽  
Clément Stark ◽  
Mark Sykes ◽  
Jochen Hinkelbein
Keyword(s):  
Interplanetary Space ◽  
Space Mission ◽  
Environmental Challenges ◽  
Surgical Case ◽  
Near Future

This focused review summarizes the medical, logistical and environmental challenges that would be associated with dealing with a traumatic surgical case during an interplanetary space mission in the near future.

scholarly journals A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 – I. Quiescent, spiking states, and quasi-periodic oscillations

2020 ◽  
Vol 495 (1) ◽  
pp. 1110-1121 ◽  
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo ◽  
A Ardito ◽  
...  
Keyword(s):  
Differential Equations ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Light Curves ◽  
Stable Region ◽  
Periodic Oscillations ◽  
X Ray ◽  
Unstable Solutions ◽  
Unified View

ABSTRACT The microquasar GRS 1915+105 is known to exhibit a very variable X-ray emission on different time-scales and patterns. We propose a system of two ordinary differential equations, adapted from the Hindmarsh–Rose model, with two dynamical variables x(t), y(t), and an input constant parameter J0, to which we added a random white noise, whose solutions for the x(t) variable reproduce consistently the X-ray light curves of several variability classes as well as the development of low-frequency quasi-periodic oscillations (QPO). We show that changing only the value of J0, the system moves from stable to unstable solutions and the resulting light curves reproduce those of the quiescent classes like ϕ and χ, the δ class and the spiking ρ class. Moreover, we found that increasing the values of J0 the system induces high-frequency oscillations that evolve into QPO when it moves into another stable region. This system of differential equations gives then a unified view of the variability of GRS 1915+105 in term of transitions between stable and unstable states driven by a single input function J0. We also present the results of a stability analysis of the equilibrium points and some considerations on the existence of periodic solutions.

scholarly journals Dynamics of Satellites Around Asteroids in Presence of Solar Radiation Pressure

2015 ◽  
Vol 10 (S318) ◽  
pp. 259-264
Author(s):  
Xiaosheng Xin ◽  
Daniel J. Scheeres ◽  
Xiyun Hou ◽  
Lin Liu
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Solar Radiation Pressure ◽  
Approximate Solutions ◽  
Triaxial Ellipsoid ◽  
Stability Maps ◽  
The Stability ◽  
Near Earth Asteroids

AbstractDue to the close distance to the Sun, solar radiation pressure (SRP) plays an important role in the dynamics of satellites around near-Earth asteroids (NEAs). In this paper, we focus on the equilibrium points of a satellite orbiting around an asteroid in presence of SRP in the asteroid rotating frame. The asteroid is modelled as a uniformly rotating triaxial ellipsoid. When SRP comes into play, the equilibrium points transformed into periodic orbits termed as``dynamical substitutes". We obtain the analytical approximate solutions of the dynamical substitutes from the linearised equations of motion. The analytical solutions are then used as initial guesses and are numerically corrected to compute the accurate orbits of the dynamical substitutes. The stability of the dynamical substitutes is analysed and the stability maps are obtained by varying parameters of the ellipsoid model as well as the magnitude of SRP.

scholarly journals Stability Analysis of the Rhomboidal Restricted Six-Body Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. A. R. Siddique ◽  
A. R. Kahsif ◽  
M. Shoaib ◽  
S. Hussain
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
First Integral ◽  
Small Mass ◽  
Equilibrium Solutions ◽  
Integral Of Motion ◽  
Jacobian Constant ◽  
Zero Velocity Curves ◽  
The Masses ◽  
Uniqueness Of Equilibrium

We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2 a and 2 b . The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are m 1 = m 2 = m 0 = m and m 3 = m 4 = m ˜ . The masses m and m ˜ are written as functions of parameters a and b such that they always form a rhomboidal central configuration. The evolution of zero velocity curves is discussed for fixed values of positive masses. Using the first integral of motion, we derive the region of possible motion of test particle m 5 and identify the value of Jacobian constant C for different energy intervals at which these regions become disconnected. Using semianalytical techniques, we show the existence and uniqueness of equilibrium solutions on the axes and off the axes. We show that, for b ∈ 1 / 3 , 1.1394282249562009 , there always exist 12 equilibrium points. We also show that all 12 equilibrium points are unstable.

scholarly journals Analysis of Price Stackelberg Duopoly Game with Bounded Rationality

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Lian Shi ◽  
Yun Le ◽  
Zhaohan Sheng
Keyword(s):  
Bounded Rationality ◽  
Stackelberg Game ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Price Adjustment ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Existence And Stability ◽  
Theoretical And Numerical Analysis ◽  
Stackelberg Duopoly

The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.

scholarly journals New Analyses of Duopoly Game with Output Lower Limiters

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaohan Sheng ◽  
Jianguo Du ◽  
Qiang Mei ◽  
Tingwen Huang
Keyword(s):  
Theoretical Basis ◽  
Numerical Experiments ◽  
Financial Constraints ◽  
Control Method ◽  
Equilibrium Points ◽  
Stable Region ◽  
Economic Systems ◽  
Evolution System ◽  
Business World ◽  
The World

In the real business world, player sometimes would offer a limiter to their output due to capacity constraints, financial constraints, or cautious response to uncertainty in the world. In this paper, we modify a duopoly game with bounded rationality by imposing lower limiters on output. Within our model, we analyze how lower limiters have an effect on dynamics of output and give proof in theory why adding lower limiters can suppress chaos. We also explore the numbers of the equilibrium points and the distribution of conditioned equilibrium points. Stable region of the conditioned equilibrium is discussed. Numerical experiments show that the output evolution system having lower limiters becomes more robust than without them, and chaos disappears if the lower limiters are big enough. The local or global stability of the conditional equilibrium points provides a theoretical basis for the limiter control method of chaos in economic systems.

scholarly journals Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar
Keyword(s):  
Binary Systems ◽  
Equilibrium Points ◽  
Semimajor Axis ◽  
Three Body Problem ◽  
Out Of Plane ◽  
Elliptic Restricted Problem ◽  
The Stability ◽  
Zero Velocity Curves ◽  
Three Body ◽  
Plane Equilibrium

This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±ζ0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.

scholarly journals Conceptual interplanetary space mission design using multi-objective evolutionary optimization and design grammars

2011 ◽  
Vol 225 (11) ◽  
pp. 1253-1261
Author(s):  
A Weber ◽  
S Fasoulas ◽  
K Wolf
Keyword(s):  
Interplanetary Space ◽  
Space Mission ◽  
Mission Design ◽  
Mission Analysis ◽  
Design Concepts ◽  
Space Mission Design ◽  
Asteroid Mission ◽  
Modular Modelling ◽  
Better Than ◽  
Mission Objective

Conceptual design optimization (CDO) is a technique proposed for the structured evaluation of different design concepts. Design grammars provide a flexible modular modelling architecture. The model is generated by a compiler based on predefined components and rules. The rules describe the composition of the model; thus, different models can be optimized by the CDO in one run. This allows considering a mission design including the mission analysis and the system design. The combination of a CDO approach with a model based on design grammars is shown for the concept study of a near-Earth asteroid mission. The mission objective is to investigate two asteroids of different kinds. The CDO reveals that a mission concept using two identical spacecrafts flying to one target each is better than a mission concept with one spacecraft flying to two asteroids consecutively.

scholarly journals Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

2019 ◽  
Vol 488 (2) ◽  
pp. 1894-1907
Author(s):  
Saleem Yousuf ◽  
Ram Kishor
Keyword(s):  
Linear Stability ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Zero Velocity Curves ◽  
Three Body

ABSTRACT The important aspects of a dynamical system are its stability and the factors that affect its stability. In this paper, we present an analysis of the effects of the albedo and the disc on the zero velocity curves, the existence of equilibrium points and their linear stability in a generalized restricted three-body problem (RTBP). The proposed problem consists of the motion of an infinitesimal mass under the gravitational field of a radiating-oblate primary, an oblate secondary and a disc that is rotating about the common centre of mass of the system. Significant effects of the albedo and the disc are observed on the zero velocity curves, on the positions of equilibrium points and on the stability region. A linear stability analysis of collinear equilibrium points L1, 2, 3 is performed with respect to the mass parameter μ and albedo parameter QA of the secondary, separately. It is found that L1, 2, 3 are unstable in both cases. However, the non-collinear equilibrium points L4, 5 are stable in a finite range of mass ratio μ. After analysing the individual as well as combined effects of the radiation pressure force of the primary, the albedo force of the secondary, the oblateness of both the primary and secondary and the disc, it is found that these perturbations play a significant role in the design of the trajectories in the vicinity of equilibrium points and in the analysis of their stability property. In the future, the results obtained will improve existing results and will help in the analysis of different space missions. These results are limited to the regular symmetric disc and radiation pressure, which can be extended later.

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