Abstract
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.
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References
Miyamoto, K.: Dynamical Simulation of the Symmetric Lagrange’s Top Precession and Nutation. JSST 1(1), 11–15 (2009) (in Japanese)
Miyamoto, K.: On the Numerical Integration of Lagrange’s Top Keeping the First Integral Value Fixed. JSST 3(2), 19–23 (2011) (in Japanese)
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© 2012 Springer Tokyo
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Miyamoto, K. (2012). On a Relationship between Typical Behavior and Initial Conditions of Lagrange’s Top. In: Kim, JH., Lee, K., Tanaka, S., Park, SH. (eds) Advanced Methods, Techniques, and Applications in Modeling and Simulation. Proceedings in Information and Communications Technology, vol 4. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54216-2_7
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DOI: https://doi.org/10.1007/978-4-431-54216-2_7
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54215-5
Online ISBN: 978-4-431-54216-2
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