Phase-space volume of regions of trapped motion: multiple ring components and arcs

Abstract

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.

Transient chaos in the Sitnikov problem

“…We note that transient phenomena and the stickiness effect in problems of Celestial Mechanics were mainly studied by Benet et al (1996Benet et al ( , 1998; Efthymiopoulos et al (1999); Contopoulos et al (1999); Contopoulos and Efstathiou (2004); Sun et al (2005); Contopoulos and Patsis (2006); Benet and Merlo (2009); Simó and Vieiro (2009). Several concepts and methods on this subject are discussed in the textbook of Contopoulos (2002).…”

Computation of families of periodic orbits and bifurcations around a massive annulus

“…On the other hand we find authors, such as Stone and Balbus (1996) or Tiscareno et al (2007) working on the dynamics of disk formation, angular momentum transport, density waves or disk instability and mass transfer; or such as Longaretti (1989), Sicardy (1991) or Benet and Merlo (2009) that carried out different studies based on the data observed by spacecraft missions to planetary rings, aimed to analyze the physical properties of the rings: composition, distribution of the masses or the relation between planet resonance relationship and the stability of the rings and incomplete arcs.…”

Motion around a monopole + ring system - I. Stability of equatorial circular orbits versus regularity of three-dimensional motion

“…We have to point out that a deeper stability analysis must include the effect of microstructure in the actual planetary rings (see e.g. Merlo & Benet 2007; Murray et al 2008; Benet & Merlo 2009; Charnoz 2009; Charnoz, Salmon & Crida 2010).…”