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BACKGROUND
A robust phylogenetic hypothesis of euthyneuran gastropods, as a basis to reconstructing their evolutionary history, is still hindered by several groups of aberrant, more or less worm-like slugs with unclear phylogenetic relationships. As a traditional "order" in the Opisthobranchia, the Acochlidia have a long history of controversial placements,… (More)

We show that choreographic three bodies {x(t), x(t + T /3), x(t − T /3)} of period T on the lemniscate, x(t) = (ˆ x + ˆ ycn(t))sn(t)/(1 + cn 2 (t)) parameterized by the Jacobi's elliptic functions sn and cn with modulus k 2 = (2 + √ 3)/4, conserve the center of mass and the angular momentum, wherê x andˆy are the orthogonal unit vectors defining the plane… (More)

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 the positions of the bodies, and the triangle whose perimeters are the momenta of the bodies, are always similar (" synchronised similar triangles "). This similarity yields… (More)

We investigate three-body motion in three dimensions under the interaction potential proportional to r α (α = 0) or log r, where r represents the mutual distance between bodies, with the following conditions: (I) the moment of inertia is non-zero constant, (II) the angular momentum is zero, and (III) one body is on the centre of mass at an instant. We prove… (More)

- K. Yamashita, T. Inoue, H. Fukuda, T. Shiohama
- 2011

Integrating wind power generation into small islands has been one of the demonstration projects in Okinawa Prefecture, Japan. Since such integration could deteriorate power quality, including frequency, in an island grid, a frequency-stabilizing system using flywheels has been integrated into a small island. In order to establish a proper… (More)

- O. Sakamoto, K. Yamashita, Y. Kitauchi, T. Nanahara, T. Inoue, T. Arakaki +1 other
- ISGT Europe
- 2011

- K. Yamashita, O. Sakamoto, Y. Kitauchi, T. Nanahara, T. Inoue, T. Arakaki +1 other
- ISGT Europe
- 2011

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 the planet completely. Even in the three-body problem, in some cases, the shape of the orbit, conservation of the centre of mass and a constant of motion (the angular momentum or… (More)

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