Regularizing dynamical problems with the symplectic logarithmic Hamiltonian leapfrog



: Mikkola Seppo, Tanikawa Kiyotaka

: 2013

: Monthly Notices of the Royal Astronomical Society

: MNRAS

: 4

: 430

: 4

: 2822

: 2827

: 6

: 0035-8711

DOI: https://doi.org/10.1093/mnras/stt085


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.



Last updated on 2024-26-11 at 14:37