
SIGMA 3 (2007), 041, 14 pages nlin.SI/0703016
https://doi.org/10.3842/SIGMA.2007.041
Contribution to the Vadim Kuznetsov Memorial Issue
Phase Space of Rolling Solutions of the Tippe Top
S. Torkel Glad ^{a}, Daniel Petersson ^{a} and Stefan RauchWojciechowski ^{b}
^{a)} Dept. of Electrical Engineering, Linköpings Universitet
SE581 83 Linköping, Sweden
^{b)} Department of Mathematics, Linköpings Universitet, SE581 83 Linköping, Sweden
Received September 15, 2006, in final form February 05, 2007; Published online March 09, 2007
Abstract
Equations of motion of an axially symmetric sphere rolling and sliding
on a plane are usually taken as model of the tippe top.
We study these equations in the nonsliding regime both in the vector
notation and in the Euler angle variables when they admit
three integrals of motion that are linear and quadratic in momenta.
In the Euler angle variables (θ,φ,ψ) these integrals give separation
equations
that have the same structure as the equations
of the Lagrange top. It makes it possible to describe the whole
space of solutions by representing them in the space of parameters
(D,λ,E) being constant values of the integrals of motion.
Key words:
nonholonomic dynamics; rigid body; rolling sphere; tippe top; integrals of motion.
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