Dynamics of an inverting Tippe Top
2014 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, Vol. 10, no 017Article in journal (Refereed) Published
We study an equivalent integrated form of the Tippe Top (TT) equations that leads to the Main Equation for the Tippe Top (METT), an equation describing time evolution of the inclination angle θ(t) of inverting TT. We study how the effective potential V(cos θ, D, λ) in METT deforms as TT is inverting and show that its minimum moves from a neighborhood of θ = 0 to a neighborhood of θ = π. We analyse behaviour of θ(t) and show that it oscillates and moves toward θ = π when the physical parameters of the TT satisfy 1 − α2 < γ < 1 and the initial conditions are such that Jellett’s integral satisfy
. Estimates for maximal value of the oscillation period of θ(t) are given.
Place, publisher, year, edition, pages
2014. Vol. 10, no 017
Tippe top, rigid body, nonholonomic mechanics, integrals of motion, gliding friction
IdentifiersURN: urn:nbn:se:liu:diva-88315DOI: 10.3842/SIGMA.2014.017ISI: 000334516500001OAI: oai:DiVA.org:liu-88315DiVA: diva2:602360