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The paper deals with the dynamics and motion planning for a rolling system with variable inertia. In a simplified formulation, the driving principle for the system under consideration is based on controlling the position of the center of mass of the object, exploiting non-holonomic rolling constraint to propel the hemisphere. We derive the dynamic model of this system and establish the condition of motion realizability. Providing that this condition holds true, we derive an approximate analytical solution for the trajectory of the particle, driving the system along a pre-specified path in the contact coordinates. The approximation is based on ignoring the quadratic velocity terms in the dynamic equations.