An analytically treatable model of long-term dynamics in a mean motion resonance with coexisting resonant modes

Efimov, Sergey; Сидоренко, В. В.

doi:10.1007/s10569-020-09965-5

Cited by 8 publications

(10 citation statements)

References 26 publications

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“…Orbit flips caused by the eccentric von Zeipel-Lidov-Kozai effect (Naoz et al 2011;Li et al 2014aLi et al , 2014bKatz et al 2011) are interpreted as a resonance phenomenon where the critical argument σ = h + sign(H)g is librating around zero or π (Sidorenko 2018a). Based on such a viewpoint, in this section we further study the problem of orbit flips by taking advantage of perturbation treatments (Wisdom 1985;Neishtadt 1987;Neishtadt & Sidorenko 2004;Sidorenko et al 2014;Saillenfest et al 2016;Efimov & Sidorenko 2020).…”

Section: Perturbative Treatmentsmentioning

confidence: 99%

“…When facing the evolution associated with the fast DOF, the variables associated with the slow DOF can be treated as parameters (Neishtadt 1987;Wisdom 1985). Such an approximation "fixing the slow variables by steps" has been applied to different contexts (Henrard & Lemaître 1987;Henrard & Caranicolas 1989;Yokoyama 1996;Milani & Baccili 1998;Sidorenko et al 2014;Sidorenko 2018bSidorenko , 2020Efimov & Sidorenko 2020;Saillenfest et al 2016Saillenfest et al , 2017Saillenfest 2020). During the timescale of the fast DOF, the variables (σ 1 , Σ 1 ) associated with the slow DOF are considered parameters, thus the subsystem associated with the fast DOF becomes integrable.…”

Section: Perturbative Treatmentsmentioning

confidence: 99%

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A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

Lei

2022

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The problem of orbit flips caused by eccentric von Zeipel–Lidov–Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system theory (periodic orbits and invariant manifolds), and perturbation treatments. Poincaré sections show that orbit flips are due to the existence of islands of libration centered at inclination of 90°, dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced, and they are in excellent agreement with one another. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasiperiodic trajectory around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectory, and resonant width measures the size of flipping regions.

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Section: Perturbative Treatmentsmentioning

confidence: 99%

Section: Perturbative Treatmentsmentioning

confidence: 99%

A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

Lei

2022

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show abstract

“…Orbit flips caused by the eccentric von Zeipel-Lidov-Kozai effect (Naoz et al 2011;Li et al 2014a,b;Katz et al 2011) are interpreted as a resonance phenomenon where the critical argument σ = h + sign(H)g is librating around zero or π (Sidorenko 2018a). Based on such a viewpoint, in this section we further study the problem of orbit flips by taking advantage of perturbation treatments (Wisdom 1985;Neishtadt 1987;Neishtadt & Sidorenko 2004;Sidorenko et al 2014;Saillenfest et al 2016;Efimov & Sidorenko 2020).…”

Section: Perturbative Treatmentsmentioning

confidence: 99%

“…When facing the evolution associated with the fast DOF, the variables associated with the slow DOF can be treated as parameters (Neishtadt 1987;Wisdom 1985). Such an approximation "fixing the slow variables by steps" has been applied to different contexts (Henrard & Lemaître 1987;Yokoyama 1996;Henrard & Caranicolas 1989;Milani & Baccili 1998;Sidorenko et al 2014;Sidorenko 2018bSidorenko , 2020Efimov & Sidorenko 2020;Saillenfest et al 2016Saillenfest et al , 2017Saillenfest 2020). During the timescale of the fast DOF, the variables (σ 1 , Σ 1 ) associated with the slow DOF are considered as parameters, thus the subsystem associated with the fast DOF becomes integrable.…”

Section: Perturbative Treatmentsmentioning

confidence: 99%

“…Furthermore, when the Hamiltonian H is given, the motion of test particles takes place on the level curves of S(H, σ 1 , Σ 1 ). Naturally, the phase portraits can be produced by plotting level curves of S in the (σ 1 , Σ 1 ) space with given Hamiltonian H (Wisdom 1985;Henrard & Caranicolas 1989;Henrard 1990;Neishtadt & Sidorenko 2004;Sidorenko et al 2014;Sidorenko 2018b,a;Efimov & Sidorenko 2020). The resulting phase portraits can be used to reveal dynamical structures in the phase space.…”

Section: Leimentioning

confidence: 99%

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A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects

Lei

2022

Preprint

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The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system theory (periodic orbits and invariant manifolds) and perturbation treatments. Poincaré sections show that orbit flips are due to the existence of islands of libration centered at inclination of 90 • , dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced and they are in excellent agreement with each other. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasi-periodic trajectories around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectories and resonant width measures the size of flipping regions.

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The resonance perturbations of the (39991) Iochroma family

Rosaev

2022

Celest Mech Dyn Astron

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An analytically treatable model of long-term dynamics in a mean motion resonance with coexisting resonant modes

Cited by 8 publications

References 26 publications

A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects

The resonance perturbations of the (39991) Iochroma family

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