scholarly journals Erratum: Kozai mechanism inside mean motion resonances in the 3-dimensional phase space

2020 ◽  
Vol 496 (4) ◽  
pp. 4646-4646
Author(s):  
Yi Qi ◽  
Anton de Ruiter
Keyword(s):  
Phase Space ◽  
Mean Motion Resonances ◽  
3 Dimensional ◽  
Mean Motion ◽  
Dimensional Phase Space

Kozai mechanism inside mean motion resonances in the three-dimensional phase space

2020 ◽  
Vol 493 (4) ◽  
pp. 5816-5824 ◽  
Author(s):  
Yi Qi ◽  
Anton de Ruiter
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Resonant Coupling ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
3D Space ◽  
Test Particles ◽  
Dimensional Phase Space ◽  
Three Body

ABSTRACT In this paper, we investigate the Kozai mechanism inside the inclined mean motion resonance (MMR) through a three-dimensional (3D) phase space. The Hamiltonian approximation for both prograde and retrograde MMRs is established by a semi-analytical method. We pick Jupiter as the disturber and study the Kozai mechanism in the Sun–Jupiter circular restricted three-body problem. Kozai islands of the prograde and retrograde MMRs are found in the 3D phase space. Numerical integration demonstrates that the locus of the orbit on the Kozai island is bounded by the Kozai island in the 3D phase space, so the orbit is locked in the Kozai+MMR state. The study of the Kozai dynamics inside a retrograde 1:1 MMR indicates that Kozai islands in the 3D phase space are just a sufficient condition for the Kozai+MMR mechanism rather than a necessary condition. There is no Kozai island in the 3D space for the retrograde 1:1 MMR, but the resonant coupling of Kozai with the retrograde 1:1 MMR appears in the phase space. Finally, dynamical behaviours of the two test particles located on Kozai islands are demonstrated in the ephemeris model.

The analysis of parameters quasi-attractors of meteofactors as a homeostatic system

2015 ◽  
Vol 9 (4) ◽  
pp. 0-0
Author(s):  
Проворова ◽  
O. Provorova ◽  
Филатова ◽  
O. Filatova ◽  
Русак ◽  
...  
Keyword(s):  
Phase Space ◽  
System Parameter ◽  
Meteorological Parameters ◽  
Vascular System ◽  
Meteorological Factors ◽  
Life Quality ◽  
3 Dimensional ◽  
Dimensional Phase Space ◽  
Weather And Climate ◽  
Cardio Vascular

Climatic and ecological environmental factors constitute the objective and subjective sides of life quality. The influence of weather and climate for health is very important. As the complex system is considered a model of 3-dimensional phase space, a box, inside of this is a quasi-attractor behavior parameters of meteo environment. The paper deals with the comparative analysis of the dynamics of meteorological factors of environment in the phase space of states in the framework of the theory of chaos and stochastic laws. The authors used their own program on the example of two territorial zones - an average strip of Russia and the Northern territory (n. Nizhnesortymsky Khanty-Ugra). It is important to note that the air temperature as an essential feature, it is practically not manifested itself in assessing the importance of parameters for Samara in contrast to Nizhnesortymsk. The used method allowed to determine the parameters of the order and to their ranking and to identify the most important characteristics in a comparative perspective the two territorial zones. It was postulated the equality between weather a climate parameters and cardio-vascular system parameter. It is postulated that the dynamics of meteorological parameters is similar to the dynamics of the cardiovascular system.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nicolas Crouseilles ◽  
Paul-Antoine Hervieux ◽  
Yingzhe Li ◽  
Giovanni Manfredi ◽  
Yajuan Sun
Keyword(s):  
Phase Space ◽  
Maxwell Equations ◽  
Stimulated Raman Scattering ◽  
Extended Phase ◽  
Five Dimensions ◽  
Particle In Cell ◽  
Spin Effects ◽  
Dimensional Phase Space ◽  
Spin Polarized ◽  
Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

scholarly journals Motion of dust in mean motion resonances with planets

2009 ◽  
Vol 103 (4) ◽  
pp. 343-364 ◽  
Author(s):  
Pavol Pástor ◽  
Jozef Klačka ◽  
Ladislav Kómar
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion

scholarly journals Planets in Mean-Motion Resonances and the System Around HD45364

2018 ◽  
pp. 2693-2711
Author(s):  
Alexandre C. M. Correia ◽  
Jean-Baptiste Delisle ◽  
Jacques Laskar
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion

scholarly journals Dynamics of Comets

1992 ◽  
Vol 152 ◽  
pp. 255-268 ◽  
Author(s):  
A. Carusi ◽  
G.B. Valsecchi
Keyword(s):  
Molecular Clouds ◽  
Vertical Component ◽  
The Sun ◽  
Giant Molecular Clouds ◽  
Mean Motion Resonances ◽  
Galactic Field ◽  
Mean Motion ◽  
Short Period ◽  
Gravitational Processes

The gravitational processes affecting the dynamics of comets are reviewed. At great distances from the Sun the motion of comets is primarily affected by the vertical component of the galactic field, as well as by encounters with stars and giant molecular clouds. When comets move in the region of the planets, encounters with these can strongly affect their motion. A good fraction of all periodic comets spend some time in temporary libration about mean motion resonances with Jupiter; some comets can be captured by this planet as temporary satellites. Finally, there is a small number of objects with orbital characteristics quite different from those of all other short-period comets.

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