Frequency Modified Fourier Transform and its Application to Asteroids

Sidlichovsky, M.; Nesvorný, David

doi:10.1007/978-94-011-5510-6_9

Cited by 42 publications

(32 citation statements)

References 3 publications

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“…We compute a chaotic observable zone as follows: we consider a set of orbits with initial conditions (I 1 (0), I 2 (0), ϕ 1 (0), ϕ 2 (0)) in a neighbourhoud of (I 1 , ϕ 1 ) = (0, π), with ϕ 2 (0), ϕ 3 (0) = 0 and I 2 (0) is chosen so that the frequency of the angle ϕ 2 isω 2 . This frequency is numerically computed using a variant (Sidlichovský and Nesvorný 1997) of the Laskar et al (1992) frequency analysis algorithm. 2 We numerically compute the motions over a timet and we consider the Poincaré section on ϕ 3 .…”

Section: Measure Of the Exponential Splitting Of The Homoclinic Tanglementioning

confidence: 99%

A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems

Lega

Guzzo

Froeschlé

2010

Celest Mech Dyn Astr

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Using a three degrees of freedom quasi-integrable Hamiltonian as a model problem, we numerically compute the unstable manifolds of the hyperbolic manifolds of the phase space related to single resonances. We measure an exponential dependence of the splitting of these manifolds through many orders of magnitude of the perturbing parameter. This is an indirect numerical verification of the exponential decay of the normal form, as predicted by the Nekhoroshev theorem. We also detect different transitions in the topology of these manifolds related to the local rational approximations of the frequencies. The variation of the size of the homoclinic tangle as well as the topological transitions turn out to be correlated to the speed of Arnold diffusion

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Section: Measure Of the Exponential Splitting Of The Homoclinic Tanglementioning

confidence: 99%

A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems

Lega

Guzzo

Froeschlé

2010

Celest Mech Dyn Astr

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“…Using the result of this numerical integration, we parametrized e as a function of − 6 . The initial phase and frequency of 6 were extracted from the output of the integration by a Fourier-based technique (Šidlichovský and Nesvorný, 1997). Specifically, we found that e ≈ 0.15 − 0.05 cos( − 6 ).…”

Section: Fall Statistics For Isotropic Ejection Velocitiesmentioning

confidence: 99%

Express delivery of fossil meteorites from the inner asteroid belt to Sweden

Nesvorný¹,

Vokrouhlický²,

Bottke³

et al. 2007

Icarus

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“…For this purpose we use the FMFT code by Sidlichovsky and Nesvorny (1997) to find the fundamental frequencies m x , m y , m z of the oscillations of the orbits along the x; y; z axes. Notice that these frequencies are measured in units of the inverse radial period of each particular orbit, as in the case of the L j .…”

Section: Self-consistent Models Of Elliptical Galaxiesmentioning

confidence: 99%

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

Kalapotharakos

Voglis

2005

Celestial Mech Dyn Astr

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We compare two different N-body models simulating elliptical galaxies. Namely, the first model is a non-rotating triaxial N-body equilibrium model with smooth center, called SC model. The second model, called CM model, is derived from the SC by inserting a central mass in it, so that all possible differences between the two models are due to the effect of the central mass. The central mass is assumed to be mainly due to a massive central black hole of mass about 1% of the total mass of the galaxy. By using the fundamental frequency analysis, the two systems are thoroughly investigated as regards the types of orbits described either by test particles, or by the real particles of the systems at all the energy levels. A comparison between the orbits of test particles and the orbits of real particles at various energy levels is made on the rotation number plane. We find that extensive stable regions of phase space, detected by test particles remain empty, i.e. these regions are not occupied by real particles, while many real particles move in unstable regions of phase space describing chaotic orbits. We run self-consistently the two models for more than a Hubble time. During this run, in spite of the noise due to small variations of the potential, the SC model maintains (within a small uncertainly) the number of particles moving on orbits of each particular type. In contrast, the CM model is unstable, due to the large amount of mass in chaotic motion caused by the central mass. This system undergoes a secular evolution towards an equilibrium state. During this evolution it is gradually self-organized by converting chaotic orbits to ordered orbits mainly of the short axis tube type approaching an oblate spheroidal equilibrium. This is clearly demonstrated in terms of the fundamental frequencies of the orbits on the rotation number plane and the time evolution of the triaxiality index.

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Frequency Modified Fourier Transform and its Application to Asteroids

Cited by 42 publications

References 3 publications

A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems

A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems

Express delivery of fossil meteorites from the inner asteroid belt to Sweden

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

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