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Analytical Solution of the Frenet-Serret Systems of Circular Motion Bodies

In this paper, the general Frenet-Serret system of circular motion body with constant velocity is analytically solved in three dimensional space. The tangent, normal, and binormal vectors are found by reducing the system into a high order ordinary differential equation. Solving this equation gives a closed form of those vectors. A special case of four dimensional Frenet-Serret system is also solved in this work.