The Lagrange Top and the Foucault Pendulum in Observed Variables

摘要

When investigating the dynamics of solids for rotation around a fixed point in the case of the dynamic symmetry A = B ≠ C (A, B, and C are the principal moments of inertia of the solid with respect to a fixed point), Euler's angles θ, ψ, and φ are more often used [1]. Because of a singularity at the point θ = 0, Euler's angles are unsuitable and it is necessary to introduce new variables. As such variables, we introduced [1] the socalled observed variables: the Cartesian coordinates of the unit vector e of the top directed along its axis of dynamic symmetry (Fig. 1). When these variables are used for description, it is possible to carry out an analogy to the motion of the Foucault pendulum [2] (Fig. 2).