22 citations · 69 across the 13 of their papers we have counts for
13 papers
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…
Morse index for figure-eight choreographies of the planar equal mass three-body problem
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
We report on numerical calculations of Morse index for figure-eight choreographic solutions to a system of three identical bodies in a plane interacting through homogeneous potenti…
Figure-eight choreographies of the equal mass three-body problem with Lennard-Jones-type potentials
Hiroshi Fukuda, Toshiaki Fujiwara, Hiroshi Ozaki
We report on figure-eight choreographic solutions to a system of three identical particles interacting through a potential of Lennard-Jones type, where is a di…
Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki +1
Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, for , a motion having constant configurat…
Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki +1
Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure μ=\sqrt{I}U, which is the product of square root of the moment o…
Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki +1
Donald Saari conjectured that the -body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure is a scale invariant pro…
Three-Body Choreographies in Given Curves
Hiroshi Ozaki, Hiroshi Fukuda, Toshiaki Fujiwara
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of…
Synchronised Similar Triangles for Three-Body Orbit with Zero Angular Momentum
Toshiaki Fujiwara, Hiroshi Fukuda, Atsushi Kameyama +2
Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are…
Evolution of the Moment of Inertia of Three-Body Figure-Eight Choreography
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
We investigate three-body motion in three dimensions under the interaction potential proportional to r^alpha (alpha \neq 0) or log r, where r represents the mutual distance between…
Choreographic Three Bodies on the Lemniscate
Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki
We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic…