Grygor'yeva L. Computer technologies in free magnet dynamics modeling

Thesis is devoted to development of new mathematical models of free magnetically interacting bodies and application of new computer technologies to model building and model analysis. Different systems of free magnetically interacting bodies are investigated: pendulums (bodies with fixed point) with magnetic/electric interaction, two free bodies system with interaction of two long cylindrical magnets, system "superconductive ring - dipole" with respect to different kinds of disposition and fixation of one of them, "garland" of free bodies that magnetically interact by their superconductive rings. For concerned systems mathematical dynamic models are built, motion stability is investigated, numerical solutions, solution plots and phase portraits for different parameter sets and initial conditions are obtained. Automatic procedures created on the basis of computer algebra system Maple 12 allow avoiding errors while conducting modeling, making cumbersome symbolic calculations of magnetic forces and obtaining graphic material for system analysis by means of visualization tools.