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Numerical Range for Orbits Under a Central Force

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Abstract

We present an explicit form for the central force that describes the orbit of some roulette curve, and interpret the orbit of the roulette curve as an algebraic curve F(1, x, y) = 0 associated to the homogeneous polynomial F(t, x, y) of a matrix A. The hodograph of the orbit is obtained as the boundary generating curve of the numerical range of A.

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Taipei, 11102, Taiwan

    Mao-Ting Chien

  2. Department of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University, Hirosaki, 036-8561, Japan

    Hiroshi Nakazato

Authors
  1. Mao-Ting Chien
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  2. Hiroshi Nakazato
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Correspondence to Mao-Ting Chien.

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Chien, MT., Nakazato, H. Numerical Range for Orbits Under a Central Force. Math Phys Anal Geom 13, 315–330 (2010). https://doi.org/10.1007/s11040-010-9082-y

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  • DOI: https://doi.org/10.1007/s11040-010-9082-y

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