Abstract
Characterizing the dynamics of heavy symmetric tops is essential in several fields of theoretical and applied physics. Accordingly, a series of approaches have been developed to describe their motion. In this paper, we present a derivation based on elementary geometric considerations carried out in the laboratory frame. Our framework enabled the simple derivation of the equation of motion for small nutations. The introduced formalism is also employed to determine the alteration of the dynamics of heavy, symmetric, spinning tops in a rotating force field, that is compared to the precession characteristics of a quantum magnetic dipole in rotating magnetic field.
Highlights
Mainstream methods for determining the equation of motion of heavy symmetric tops can be classified according to the theoretical approaches used, and the reference frames applied
Euler angles offer a natural parametrization of the rigid body attitude revealing the first integrals within the framework of the Lagrangian formalism
The dynamics of a heavy symmetric top is determined by the constants of motion Ln, Lz and E
Summary
Mainstream methods for determining the equation of motion of heavy symmetric tops can be classified according to the theoretical approaches used, and the reference frames applied. A, with rate of change A_ its nutation motion, ΔA_, can be described as that of a time dependent geometric vector viewed from the purely precessing reference frame rotating with ωp(u0)z. We will limit our investigation to the situation when the precession is in synchrony with the driving field, meaning, that the rotating component of the field stays in the same vertical plane as the symmetry axis In these special circumstances, the equations connecting kinematic and dynamic quantities such as Eqs 10 and 11 are not affected by the particularities of the field. Note that if no horizontal rotating component is present S precesses with the Larmor frequency ωL cB (See Spin in Magnetic Field in the Supplementary Material) In this special case the attitude of S is arbitrary, i.e., determined by the initial condition. The magnitude oscillations described by Eq 19 are not present in the case of spins
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