Glad, S. Torkel; Petersson, Daniel; Rauch-Wojciechowski, Stefan Phase space of rolling solutions of the tippe top. (English) Zbl 1131.70003 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 041, 14 p. (2007). Summary: 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 \(\theta,\phi,\psi\) these integrals give separation of equations that have the same structure as the equations of Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters \(D,\lambda,E\) being constant values of the integrals of motion. Cited in 5 Documents MSC: 70E18 Motion of a rigid body in contact with a solid surface 70E40 Integrable cases of motion in rigid body dynamics 70F25 Nonholonomic systems related to the dynamics of a system of particles Keywords:integrals of motion; nonsliding regime; Euler angle variables PDFBibTeX XMLCite \textit{S. T. Glad} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 041, 14 p. (2007; Zbl 1131.70003) Full Text: DOI arXiv EuDML EMIS