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Regularizing dynamical problems with the symplectic logarithmic Hamiltonian leapfrog
Tekijät: Mikkola Seppo, Tanikawa Kiyotaka
Julkaisuvuosi: 2013
Journal: Monthly Notices of the Royal Astronomical Society
Lehden akronyymi: MNRAS
Numero sarjassa: 4
Vuosikerta: 430
Numero: 4
Aloitussivu: 2822
Lopetussivu: 2827
Sivujen määrä: 6
ISSN: 0035-8711
DOI: https://doi.org/10.1093/mnras/stt085
Tiivistelmä
The logarithmic Hamiltonian leapfrog algorithm solves the two-body
problem with only a phase error. This is true independent of orbital
eccentricity and thus it provides an algorithmic regularization. The
algorithm gives regular results even for collision orbits when the
potential is of 1/r type and it can be used for substeps in connection
with extrapolation methods to obtain high accuracy. This applies also in
problems in which there are many 1/r-type singularities, such as the
few-body problem. A new surprising result is that a simple modification
of the logarithmic leapfrog produces exact trajectories also for the
quasi-Keplerian problem with a 1/r^2 term in the potential.
The logarithmic Hamiltonian leapfrog algorithm solves the two-body
problem with only a phase error. This is true independent of orbital
eccentricity and thus it provides an algorithmic regularization. The
algorithm gives regular results even for collision orbits when the
potential is of 1/r type and it can be used for substeps in connection
with extrapolation methods to obtain high accuracy. This applies also in
problems in which there are many 1/r-type singularities, such as the
few-body problem. A new surprising result is that a simple modification
of the logarithmic leapfrog produces exact trajectories also for the
quasi-Keplerian problem with a 1/r^2 term in the potential.
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