22 citations · 85 across the 23 of their papers we have counts for
23 papers
Fold of a bifurcation solution from the figure-eight choreography in the three body problem
Hiroshi Fukuda, Hiroshi Ozaki
In the figure-eight choreography in the classical three-body problem, both-side bifurcation solutions sometimes fold on one side of the bifurcation point with cusp of action. Three…
Bifurcation analysis of figure-eight choreography in the three-body problem based on crystallographic point groups
Hiroshi Fukuda, Hiroshi Ozaki
The bifurcation of figure-eight choreography is analyzed by its symmetry group based on the variational principle of the action. The irreducible representations determine the symme…
Variational principle of action and group theory for bifurcation of figure-eight solutions
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
Figure-eight solutions are solutions to planar equal mass three-body problem under homogeneous or inhomogeneous potentials. They are known to be invariant under the transformation…
Variational principle for bifurcation in Lagrangian mechanics
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
An application of variational principle to bifurcation of periodic solution in Lagrangian mechanics is shown. A few higher derivatives of the action integral at a periodic solution…
Morse index and bifurcation for figure-eight choreographies of the equal mass three-body problem
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
We report on the Morse index and periodic solutions bifurcating from the figure-eight choreography for the equal mass three-body problem under homogeneous potential for $a…
Decomposition of the Hessian matrix for action at choreographic three-body solutions with figure-eight symmetry
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
We developed a method to calculate the eigenvalues and eigenfunctions of the second derivative (Hessian) of action at choreographic three-body solutions that have the same symmetri…