Mechanics of a particle near the center of a rotating ring: Hiroshi Okamura, Department of Physics, University of Tokyo, Tokyo, Japan and Department of Physics, Faculty of General Education, Kogakuin University, Shinjuku, Tokyo, Japan; Tadayuki Ohta, Department of Mathematical Physics, College of Technology, Seikei University, Musashino, Tokyo, Japan; Toshiei Kimura, Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken, Japan; and Kichiro Hiida, Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, Japan