On a Relationship between Typical Behavior and Initial Conditions of Lagrange’s Top
The parameterα, which at first was introduced to modify the coordinate of the equilibrium point of Euler’s equations, 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.
KeywordsEquilibrium Point Potential Function Euler Angle Typical Behavior Typical Motion
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