Abstract
Formal explanations of the dynamics of free and heavy tops are considered to be known for centuries. However, intuitive understanding of their unexpected behavior is still a challenge. In this paper, we present elementary force based explanations of several phenomena related the dynamics of heavy symmetric tops, derived in inertial and non-inertial reference frames. Simple calculations are enabled by a model equivalent to a spinning top, namely a square-formed tube carrying a streaming ideal fluid or a frictionless chain. Precession in a combined, gravitational and magnetic field is also discussed.
Highlights
Interpreting the wobble of a torque-free spinning plate, the rise of a tippe top, as well as the precession of a fast spinning wheel suspended at the extremity of its axle and exposed to gravitational or electromagnetic torque, inspired the brightest researchers during the past centuries
Deeper understanding of torque-induced precession would be important for teaching a series of its applications, like the gyroscope, electron spin resonance (ESR) [9] and nuclear magnetic resonance (NMR) [10, 11]
The proposed model consists of a heavy chain or fluid which frictionlessly circulates in a closed loop determined by a square-shaped tube, and an angular momentum will arise
Summary
Interpreting the wobble of a torque-free spinning plate, the rise of a tippe top, as well as the precession of a fast spinning wheel suspended at the extremity of its axle and exposed to gravitational or electromagnetic torque, inspired the brightest researchers during the past centuries. Our model relies on a square-shaped rigid tube with a heavy fluid or chain in its interior, which is allowed to circulate smoothly and without resistance in the closed loop determined by the rigid tube This flow generates an angular momentum enabling the comparison of the novel configuration to the classical heavy tops which are symmetric, spinning objects. Note that different points of a freely precessing body are subjected to acceleration which varies in space and time, mechanical tensions will arise within precessing free tops This phenomenon has a major importance in planetary physics [20] (see Supplementary Section II.D). We only investigate the pure precession (steady nutation angle) of symmetric tops exposed to a torque (“heavy” tops), where dissipation is neglected
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