Related papers: Tippe Top Equations and Equations for the Related …
The existing results about inversion of a tippe top (TT) establish stability of asymptotic solutions and prove inversion by using the LaSalle theorem. Dynamical behaviour of inverting solutions has only been explored numerically and with…
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…
The dynamical equations for a gliding Lagrange top are not integrable. They have 5 dynamical variables and admit one integral of motion. We show that all solutions go to one of the two vertical spinning solutions and determine conditions of…
We reexamine a very classical problem, the spinning behavior of the tippe top on a horizontal table. The analysis is made for an eccentric sphere version of the tippe top, assuming a modified Coulomb law for the sliding friction, which is a…
We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced…
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
Asymptotic behaviour of a tippe top, under the action of gliding friction. Liapunov stability analysis of the asymptotics of states with arbitrary initial conditions.
We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the…
Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…
A toy top is defined as a rotationally symmetric body moving in a constant gravitational field while one point on the symmetry axis is constrained to stay in a horizontal plane. It is an integrable system similar to the Lagrange top.…
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the…
In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is described not only by the force applied at the contact point, but also…
The rise of the top is studied by considering slipping friction. For this case, equations of motion are obtained by using Euler equations for a heavy symmetric top with a hemispherical peg. Different situations are considered to see how the…
The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video. As an asymmetrical top, its motion is completely described by the Euler…
We investigate the dynamics of a sliding top that is a rigid body with an ideal sharp tip moving in a perfectly smooth horizontal plane, so no friction forces act on the body. We prove that this system is integrable only in two cases…
The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for…
The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disk, being reminiscent to (but different from) the well-known inversion of the…
Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…