Related papers: How does a heavy symmetric top rise?
The dissipative motion and the rise of a heavy symmetrical top with a hemispherical peg are studied. A model taking the fixed point of the top as the center of the peg is considered when the top completely slips and the rolling motion is…
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.…
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…
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…
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…
There are various types of motion of a heavy symmetric top like regular precession, cusp like motion, rise of the top, etc. One of the tools used to understand that motion is effective potential. The effective potential for a spinning heavy…
A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the…
In this work we consider a heavy symmetrical top whose pivot is subjected to vertical and horizontal vibrations, and derive a resonance criterion when the top is thrown off the stable position.
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…
I discuss the precession motion of a symmetrical top without the assumption that its precessional velocity is much smaller than its spin angular velocity. I derive the general formula for the precessional velocity in an elementary way and…
We describe a new type of top, the twisted top, obtained by appending a cocycle to the Lie-Poisson bracket for the charged heavy top, thus breaking its semidirect product structure. The twisted top has an integrable case that corresponds to…
New method of analysing the free and heavy symmetric tops using Euler's equations to perform extraction from the body frame to the lab frame. Subsequent to extraction, the lab frame equations are solved by space phasor method.
Three aspects of supersymmetric theories are discussed: electroweak symmetry breaking, the issues of flavor, and gauge unification. The heavy top quark plays an important, sometimes dominant, role in each case. Additional symmetries lead to…
The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type…
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,…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
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.…
Recently, Morrison and Updike showed that many dissipative systems are naturally described as possessing a Riemann curvature-like bracket, which similar to the Poisson bracket, generates the dissipative equations of motion once suitable…
A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…
Dynamical models of inflation are given with composite inflatons by means of massive supersymmetric gauge theory. Nearly flat directions and stable massive ones in the potential are identified and slow-roll during inflation is examined.…