On a Relationship between Typical Behavior and Initial Conditions of Lagrange’s Top

  • Kazumasa Miyamoto
Conference paper
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 4)


The parameterα, which at first was introduced to modify the coordinate of the equilibrium point of Euler’s equations[1], is used to represent the canonical equations of (θ, p θ ) for Lagrange’s top. We then take a perspective approach to the top by doing an analysis of the potential function U(θ, α), and settle on a mapping between typical motions of the top and the values of α. This approach makes it clear that there are two different modes of stationary precession and that a sleeping top mode can be reduced from a Lagrange’s top.


Equilibrium Point Potential Function Euler Angle Typical Behavior Typical Motion 
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  1. 1.
    Miyamoto, K.: Dynamical Simulation of the Symmetric Lagrange’s Top Precession and Nutation. JSST 1(1), 11–15 (2009) (in Japanese) Google Scholar
  2. 2.
    Miyamoto, K.: On the Numerical Integration of Lagrange’s Top Keeping the First Integral Value Fixed. JSST 3(2), 19–23 (2011) (in Japanese) Google Scholar

Copyright information

© Springer Tokyo 2012

Authors and Affiliations

  • Kazumasa Miyamoto
    • 1
  1. 1.Faculty of Health and Welfare, Department of Healthcare InformaticsTakasaki University of Health and WelfareTakasakiJapan

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