%0 Generic %1 citeulike:46673 %A Fujiwara, Toshiaki %A Fukuda, Hiroshi %A Ozaki, Hiroshi %D 2003 %K choreography evolution inertia moment %T Evolution of the Moment of Inertia of Three-Body Figure-Eight Choreography %U http://arxiv.org/abs/math-ph/0304014 %X We investigate three-body motion in three dimensions under the interaction potential proportional to r^alpha (alpha 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 that the motion which satisfies conditions (I)-(III) with equal masses for alpha -2, 2, 4 is impossible. And motions which satisfy the same conditions for alpha=2, 4 are solved explicitly. Shapes of these orbits are not figure-eight and these motions have collision. Therefore non-conservation of the moment of inertia for figure-eight choreography for alpha -2 is proved. We also prove that the motion which satisfies conditions (I)-(III) with general masses under the Newtonian potential alpha=-1 is impossible.

@misc{citeulike:46673, abstract = {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 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 that the motion which satisfies conditions (I)-(III) with equal masses for alpha \neq -2, 2, 4 is impossible. And motions which satisfy the same conditions for alpha=2, 4 are solved explicitly. Shapes of these orbits are not figure-eight and these motions have collision. Therefore non-conservation of the moment of inertia for figure-eight choreography for alpha \neq -2 is proved. We also prove that the motion which satisfies conditions (I)-(III) with general masses under the Newtonian potential alpha=-1 is impossible.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Fujiwara, Toshiaki and Fukuda, Hiroshi and Ozaki, Hiroshi}, biburl = {https://www.bibsonomy.org/bibtex/26c2823552a732fff053df04c3ba9a810/a_olympia}, citeulike-article-id = {46673}, description = {citeulike}, eprint = {math-ph/0304014}, interhash = {2bcdd185809dc2387b2479d7b67c96e7}, intrahash = {6c2823552a732fff053df04c3ba9a810}, keywords = {choreography evolution inertia moment}, month = {September}, timestamp = {2007-08-18T13:22:59.000+0200}, title = {Evolution of the Moment of Inertia of Three-Body Figure-Eight Choreography}, url = {http://arxiv.org/abs/math-ph/0304014}, year = 2003 }