scholarly journals Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

2018 ◽  
Vol 27 (04) ◽  
pp. 1850036 ◽  
Author(s):  
Euaggelos E. Zotos ◽  
F. L. Dubeibe
Keyword(s):  
Test Particle ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Orbital Dynamics ◽  
Final States ◽  
Jacobi Constant ◽  
Hill Region ◽  
Large Sets ◽  
Different Types ◽  
Three Body

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or spacecraft) in the planar Sun–Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with the earlier ones regarding other planetary systems.

scholarly journals A note on the existence of invariant punctured tori in the planar circular restricted three-body problem

1988 ◽  
Vol 8 (8) ◽  
pp. 63-72 ◽  
Keyword(s):  
Body Problem ◽  
Small Mass ◽  
Connected Components ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Constant ◽  
Hill Region ◽  
The Masses ◽  
Three Body ◽  
Collision Orbits

AbstractThe existence of transversal ejection—collision orbits in the restricted three-body problem is shown to imply, via the KAM theorem, the existence, for certain intervals of (large) values of the Jacobi constant, of an uncountable number of invariant punctured tori in the corresponding (non-compact) energy surface. The proof is based on a comparison between Levi-Civita and McGehee regularizing variables. That these transversal ejection-collision orbits do actually exist was proved in [5] in the case where one of the primaries has a small mass and the zero-mass body revolves around the other (and for all values of the Jacobi constant compatible with the existence of three connected components for the Hill region); it is proved here without any restriction on the masses, well in the spirit of Conley's thesis [3].

scholarly journals Exit basins for the Sitnikov problem with variable mass

2020 ◽  
Vol 25 (1) ◽  
pp. 150-157
Author(s):  
Fredy Leonardo Dubeibe ◽  
Guillermo Alfonso Gonzalez ◽  
Edgar Acosta
Keyword(s):  
Test Particle ◽  
Initial Conditions ◽  
Numerical Study ◽  
Variable Mass ◽  
Final States ◽  
Sitnikov Problem ◽  
Final State ◽  
Oscillatory State

In the present paper, we perform a numerical study of the Sitnikov problem aiming to characterize the orbits of a variable mass particle (e.g., comet, rocket, asteroid or spacecraft) and determine the uncertainty in the prediction of the final state of the test particle. The classification of final states was done through the well-known exit basins, while the determination of the uncertainty was calculated using a new tool named Basin entropy. It is found that for small values of the initial mass of the test particle, the number of initial conditions leading to bounded orbits gets increased, thus reducing the uncertainty in the final states. The same behavior in uncertainty is observed for increasing values of the exponent in Jeans law for the variation of the mass. Our results allow us to conclude that: i) an accelerated fuel consumption in the initial stages of stabilization of a satellite can keep the object in an oscillatory state around the primaries and ii) if the mass of the satellite is less than one hundredth of the mass of each primary, it is possible to predict with a very high certainty the final state of the satellite, regardless of the accuracy in the initial conditions of the system.

The role of the mass ratio in ballistic capture

2020 ◽  
Vol 498 (1) ◽  
pp. 1515-1529
Author(s):  
Zong-Fu Luo
Keyword(s):  
Initial Conditions ◽  
Massless Particle ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Ballistic Capture ◽  
Jacobi Constant ◽  
Celestial Bodies ◽  
Three Body ◽  
Gravity System

ABSTRACT A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, that is, the Pluto–Charon, Earth–Moon, Sun–Jupiter, and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.

Orbit Taxonomy in an Electromagnetic Binary System of Two Magnetic Dipoles

2020 ◽  
Vol 30 (05) ◽  
pp. 2030011
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Binary System ◽  
Magnetic Moments ◽  
Large Data ◽  
Large Data Sets ◽  
Orbital Dynamics ◽  
Data Sets ◽  
Jacobi Constant ◽  
Magnetic Dipoles ◽  
Different Types ◽  
Starting Conditions

We elucidate the orbital dynamics of a binary system of two magnetic dipoles, by utilizing the grid classification method. Our target is to unveil how the total energy (expressed through the Jacobi constant), as well as the ratio of the magnetic moments affect the character of the trajectories of the test particle. By integrating numerically large data sets of starting conditions of trajectories in different types of 2D maps, we manage to reveal the basins corresponding to bounded, close encounter and escape motion, along with the respective time scales of the phenomena.

scholarly journals A New Formulation of a Hénon–Heiles Potential with Additional Singular Gravitational Terms

2020 ◽  
Vol 30 (13) ◽  
pp. 2050197
Author(s):  
Euaggelos E. Zotos ◽  
Wei Chen ◽  
Juan F. Navarro ◽  
Tareq Saeed
Keyword(s):  
Gravitational Potential ◽  
Test Particle ◽  
Orbital Energy ◽  
Orbital Dynamics ◽  
Transition Parameter ◽  
Different Types ◽  
Starting Conditions ◽  
New Formulation ◽  
Parameter Influence

We examine the orbital dynamics in a new Hénon–Heiles system with an additional gravitational potential, by classifying sets of starting conditions of trajectories. Specifically, we obtain the results on how the total orbital energy along with the transition parameter influence the overall dynamics of the massless test particle, as well as the respective time of escape/collision. By using modern diagrams with color codes we manage to present the different types of basins of the system. We show that the character of the orbits is highly dependent on the energy and the transition parameter.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

scholarly journals Embodied Energy and Embodied GWP of Windows: A Critical Review

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3788
Author(s):  
Francesco Asdrubali ◽  
Marta Roncone ◽  
Gianluca Grazieschi
Keyword(s):  
Critical Analysis ◽  
Strong Dependence ◽  
Primary Energy ◽  
Point Of View ◽  
Embodied Energy ◽  
Construction Sector ◽  
Industrialized Countries ◽  
Different Types ◽  
Operational Phase ◽  
Operational Impact

The construction sector is one of the most energy-intensive in the industrialized countries. In order to limit climate change emissions throughout the entire life cycle of a building, in addition to reducing energy consumption in the operational phase, attention should also be paid to the embodied energy and CO2 emissions of the building itself. The purpose of this work is to review data on embodied energy and GWP derived from EPDs of different types of windows, to identify the LCA phases, the most impacting materials and processes from an environmental point of view and to perform a critical analysis of the outcomes. The results show a strong dependence on the typology of the frame, with wooden windows having competitive performances: lower average primary energy non-renewable (1123 MJ/FU), higher average primary energy renewable (respectively 817 MJ/FU) and lower global warming potential (54 kgCO2eq/FU). More transparency and standardization in the information conveyed by the program operators is, however, desirable for a better comparability of windows performances. In particular, the inclusion of the operational impact in the EPD is sporadic, but strongly important, since it can be the most impactful phase.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

Spectral analysis of forced turbulence in a non-neutral plasma

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
S. Chen ◽  
G. Maero ◽  
M. Romé
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Final States ◽  
Self Similarity ◽  
Subsequent Formation ◽  
Electron Plasmas ◽  
Particle In Cell ◽  
Fluid Turbulence ◽  
Inviscid Incompressible Fluid ◽  
Forced Turbulence

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

Sign in / Sign up

Export Citation Format

Share Document