DYNAMICAL EXPLANATION ON TOROFLUX'S PHENOMENA

The dynamic analysis of the toroflux, a toy with torus-spring winded by a steel ribbon, is given in this paper. As two special phenomena, the toroflux can suddenly change its geometrical form, and can rotate rapidly in falling process around a cylindrical body. The topological character of a closed bent rod is applied to determine the curvature and twist of the toroflux, and the elastic potential energies of two different equilibrium states of toroflux are calculated and compared. Then the phenomena of its shape mutation can be examined by the principal of minimal elastic potential energy. Taking a circle ring as an element of the toroflux, and the stretching effect of adjacent rings is considered. The pure rolling of the ring on the cylinder in falling process is analyzed to examine the occurrence of rapidly rotation, and the angular acceleration of the toroflux in falling process is derived. The theoretical results coincide with the data by experiment.