Stability of Zitterbewegung of a rigid particle

A version of compactification of abundant spatial dimensions is suggested on the assumption that all the mechanical systems execute uniformly a Zitterbewegung which effectively reduces the number of their degrees of freedom. This is exemplified by the Zitterbewegung pattern of a rigid particle. The dynamics of the rigid particle may be taken such as to allow a (D−4)-dimensional Zitterbewegung but eliminating the possibility of a higher-dimensional Zitterbewegung which results in that the worldline of the particle turns out to be wrapped around a cylindroid with a compact (D−4)-dimensional cross section and 4-dimensional ruling. The class of Lagrangians ensuring the stability of planar a Zitterbewegung is specified.