Abstract: The general motion of a rigid body is the most complicated type of motion in rigid body

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.

Key words: rigid bodies general motion, orthogonal matrix, Chasles’theorem, Euler Angles