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.

Superconductivity and the existence of Nambu's three-dimensional phase space mechanics

1984 ◽  
Vol 104 (2) ◽  
pp. 106-108 ◽  
Author(s):  
Reinaldo Angulo ◽  
Simón Codriansky ◽  
Carlos A. Gonzalez-Bernardo ◽  
Andrés J. Kalnay ◽  
Freddy Perez-M ◽  
...  
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Space Mechanics

scholarly journals Constraining cluster masses from the stacked phase space distribution at large radii

2019 ◽  
Vol 489 (1) ◽  
pp. 1344-1356
Author(s):  
Akinari Hamabata ◽  
Masamune Oguri ◽  
Takahiro Nishimichi
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Space Distribution ◽  
Line Of Sight ◽  
Mass Dependence ◽  
Mass Measurements ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
Transverse Distance ◽  
Hubble Flow

Abstract Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two-component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $\, h^{-1}$ Mpc from cluster centres based on N-body simulations. We confirm that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line of sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2\, h^{-1}$ Mpc. We estimate that, by using 1.5 × 105 spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5 per cent if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7 per cent by improving the accuracy of the model.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

scholarly journals Features of pulsed synchronization of an autooscillatory system with a three-dimensional phase space

2006 ◽  
Vol 32 (4) ◽  
pp. 343-346 ◽  
Author(s):  
A. P. Kuznetsov ◽  
N. V. Stankevich ◽  
L. V. Tyuryukina
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space

scholarly journals Planetary and satellite three body mean motion resonances

Icarus ◽  
2016 ◽  
Vol 274 ◽  
pp. 83-98 ◽  
Author(s):  
Tabaré Gallardo ◽  
Leonardo Coito ◽  
Luciana Badano
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion ◽  
Three Body
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