kinematics， and its solution usually requires the aid of Euler's theorem or Chasles’theorem.

Through these two theorems，we can decompose the general motion of a rigid body into simpler

fixed-axis rotation and translation. This paper mainly uses the orthogonal matrix in the algebra

theory to describe the motion of a rigid body，and analyzes the eigenprob- lems of fixed-point

rotation，and proves Euler’s theorem. Then it decomposes the fixed-point rotation of a

rigid body. Physical images and derivation conclusions are given，and a simple description of the

complex general motion of rigid bodies is completed.