Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Hinse, T. C.; Christou, Apostolos; Alvarellos, J. L.; Goździewski, Krzysztof

doi:10.1111/j.1365-2966.2010.16307.x

Cited by 81 publications

(92 citation statements)

References 63 publications

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“…Later works have shown that at least the totality of the satellites known in 2003 with a precisely determined orbit (30 objects) do not escape over a very long time (Nesvorný et al 2003; see also Yokoyama et al 2003), and averaged elements were found for these satellites that show their organization in families (Nesvorný et al 2003(Nesvorný et al , 2004, an important fact that was confirmed analytically (Beaugé & Nesvorný 2007). Concerning stability studies of the phase space structure of the satellite region, numerical integrations of fictitious satellites (Carruba et al 2002;Yokoyama et al 2003;Nesvorný et al 2003;Hinse et al 2010) confirm the different dynamical portraits obtained between prograde and retrograde regions (Hénon 1969(Hénon , 1970. The study of the overall dynamical structure of the Jovian satellite region with the determination of the various important mean motion resonances for the three-body problem has been done by Hinse et al (2010).…”

Section: Introductionmentioning

confidence: 93%

“…Concerning stability studies of the phase space structure of the satellite region, numerical integrations of fictitious satellites (Carruba et al 2002;Yokoyama et al 2003;Nesvorný et al 2003;Hinse et al 2010) confirm the different dynamical portraits obtained between prograde and retrograde regions (Hénon 1969(Hénon , 1970. The study of the overall dynamical structure of the Jovian satellite region with the determination of the various important mean motion resonances for the three-body problem has been done by Hinse et al (2010).…”

Section: Introductionmentioning

confidence: 99%

“…We used long-term numerical integrations with a model taking the perturbations of the giant planets on the motion of the satellite into account, along with a chaos indicator, to precisely investigate the chaoticity of all the satellites, extending the works of Saha & Tremaine (1993), Beaugé & Nesvorný (2007), Nesvorný et al (2003) and Hinse et al (2010). The chaotic diffusion of the satellites is shown, as well as the reasons for their chaotic behavior.…”

Section: Introductionmentioning

confidence: 99%

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The long-term dynamics of the Jovian irregular satellites

Frouard

Vienne

Fouchard

2011

A&A

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Context. The dynamical region of the Jovian irregular satellites presents an interesting web of resonances that are not yet fully understood. Of particular interest is the influence of the resonances on the stochasticity of the individual orbits of the satellites, as well as on the long-term chaotic diffusion of the different families of satellites. Aims. We make a systematic numerical study of the satellite region to determine the important resonances for the dynamics, to search for the chaotic zones, and to determine their influences on the dynamics of the satellites. We also compare these numerical results to previous analytical works. Methods. Using extensive numerical integrations of the satellites along with an indicator of chaos (MEGNO), we show global and detailed views of the retrograde and prograde regions for various dynamical models of increasing complexity and indicate the appearance of the different types of resonances and the implied chaos. Results. Along with secular and mean motion resonances that shape the dynamical regions of the satellites, we report a number of resonances involving the Great Inequality, and which are present in the system thanks to the wide range of the values of frequencies of the pericenter available for the satellites. The chaotic diffusion of the satellites is also studied and shows the long-term stability of the Ananke and Carme families, in contrast to the Pasiphae family.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The long-term dynamics of the Jovian irregular satellites

Frouard

Vienne

Fouchard

2011

A&A

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“…For a long time, first-order variational equations have been widely used to calculate Lyapunov exponents and the Mean Exponential Growth of Nearby Orbits (MEGNO, Cincotta et al 2003) in the astrophysics community (Tancredi et al 2001;Hinse et al 2010). We speculate that higher-order variational equations may be able to improve such chaos indicators.…”

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confidence: 99%

Second-order variational equations forN-body simulations

Rein

Tamayo

2016

Mon. Not. R. Astron. Soc.

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First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO).In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection.We provide an implementation of first and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

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“…In NIMASTEP, we adopt the same strategy as Goździewski et al (2001) for the numerical computation of the MEGNO. This indicator has been successfully used in some papers, for instance, Breiter et al (2005), Cincotta & Simó (2000), Goździewski et al (2001Goździewski et al ( , 2008 and Hinse et al (2008Hinse et al ( , 2010. For the results concerning the MEGNO implemented into NIMASTEP we refer the reader to Valk et al (2009a) and Compère et al (2012).…”

Section: Megno: Mean Exponential Growth Factor Of Nearby Orbitsmentioning

confidence: 99%

NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

Delsate

Compère

2012

A&A

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NIMASTEP is a dedicated numerical software developed by us, which allows one to integrate the osculating motion (using Cartesian coordinates) in a Newtonian approach of an object considered as a point-mass orbiting a homogeneous central body that rotates with a constant rate around its axis of smallest inertia. The code can be applied to objects such as particles, artificial or natural satellites, or space debris. The central body can be either any terrestrial planet of the solar system, any dwarf-planet, or even an asteroid. In addition, very many perturbations can be taken into account, such as the combined third-body attraction of the Sun, the Moon, or the planets, the direct solar radiation pressure (with the central body shadow), the non-homogeneous gravitational field caused by the non-sphericity of the central body, and even some thrust forces. The simulations were performed using different integration algorithms. Two additional tools were integrated in the software package; the indicator of chaos MEGNO and the frequency analysis NAFF. NIMASTEP is designed in a flexible modular style and allows one to (de)select very many options without compromising the performance. It also allows one to easily add other possibilities of use. The code has been validated through several tests such as comparisons with numerical integrations made with other softwares or with semi-analytical and analytical studies. The various possibilities of NIMASTEP are described and explained and some tests of astrophysical interest are presented. At present, the code is proprietary but it will be released for use by the community in the near future. Information for contacting its authors and (in the near future) for obtaining the software are available on the web site http://www.fundp.ac.be/en/research/projects/ page_view/10278201/

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Application of the MEGNO technique to the dynamics of Jovian irregular satellites

Cited by 81 publications

References 63 publications

The long-term dynamics of the Jovian irregular satellites

The long-term dynamics of the Jovian irregular satellites

Second-order variational equations forN-body simulations

NIMASTEP: a software to modelize, study, and analyze the dynamics of various small objects orbiting specific bodies

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