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Mikkola, Seppo; Tanikawa, Kiyotaka

doi:10.1023/a:1008368322547

Cited by 113 publications

(76 citation statements)

References 8 publications

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“…The purpose here is to compare the performance of φ 2 h with the second order symplectic integrator of Mikkola & Tanikawa (1999) and Preto & Tremaine (1999), which we call φTrem, and leapfrog. The time step function for φTrem will be that presented in Mikkola & Tanikawa (1999). Section 2.2 shows leapfrog's conservation of all integrals of motion, except for the energy, to machine precision.…”

Section: So φmentioning

confidence: 99%

“…Nonetheless, Mikkola & Tanikawa (1999) and Preto & Tremaine (1999) independently discovered a symplectic integrator for small N collisional problems which is able to adapt its time step as a function of the total potential energy of the system. Time reversible integrators share similarities to some symplectic integrators for regular or near regular motion (Hairer et al 2006) and indeed time reversible methods for collisional systems have been developed.…”

Section: Introductionmentioning

confidence: 99%

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Symplectic integration for the collisional gravitationalN-body problem

Hernández¹,

Bertschinger²

2015

Mon. Not. R. Astron. Soc.

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We present a new symplectic integrator designed for collisional gravitational N -body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the N -body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of Yoshida. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small N collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the 4th order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the N -body problem. The integrator is a promising tool in collisional gravitational dynamics.

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Section: So φmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symplectic integration for the collisional gravitationalN-body problem

Hernández¹,

Bertschinger²

2015

Mon. Not. R. Astron. Soc.

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“…It also has a significant advantage in investigating such properties as periodic orbits and close encounters (e.g. , Broucke 1975;Broucke & Boggs 1975;Mikkola & Tanikawa 1999a). It can be integrated numerically without catastrophic errors after the Levi-Civita or KS transformation (Levi-Civita 1920; Kustaanheimo & Stiefel 1965;Stiefel & Scheifele 1971).…”

Section: General N-body Problem With Redundant Variablesmentioning

confidence: 99%

An Efficient Conservative Integrator With a Chain Regularization for the Few-Body Problem

Minesaki

2015

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We design an efficient orbital integration scheme for the general N-body problem that preserves all the conserved quantities except the angular momentum. This scheme is based on the chain concept and is regarded as an extension of a d'Alembert-type scheme for constrained Hamiltonian systems. It also coincides with the discretetime general three-body problem for particle number N = 3. Although the proposed scheme is only second-order accurate, it can accurately reproduce some periodic orbits, which cannot be done with generic geometric numerical integrators.

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“…Another way of regularizing the computation of motions is to use the logarithmic Hamiltonian (Mikkola and Tanikawa, 1999a;Preto and Tremaine, 1999). This method essentially uses a suitable time transformation algorithm, but no coordinate transformations, except possibly linear ones.…”

Section: Introductionmentioning

confidence: 99%