2002•Transactions of the Society of Instrument and Control EngineersOpen access

Rotation Representation Using an Axis Fixed on Rotational System and a Rotation Angle

Ritsuo Hasegawa

Abstract

Various mathematical models of rotation are used for various applications of engineering. Rotational motion can be described by Euler's motion equation and the angular rate vector can be obtained by solving the equation. Various differential equations by which rotation can be obtained from angular rate vector are there corresponding to the models of rotation.In some problems concerning the rotation of a spinning rocket or a satellite, the rotational axis fixed on the body may be considered. It is shown that rotation can be represented using of two parameters showing the orientation of the rotational axis fixed on rotational system and the rotation angle around the axis. Its deferential equation is derived in this paper.

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Key concepts: Rotation around a fixed axis, Euler's rotation theorem, Rotation (mathematics), Angular velocity, Euler angles, Physics, Differential rotation, Orientation (vector space)