A short-cut method for the solution of the betatron oscillation in particle accelerators is developed to obtain its smooth term and quick oscillation term in whatever order of accuracy desired.

• 本文提出加速器自由振荡近似解的简便方法,按规律能直接写出任何级近似解,并分出光滑项与快振荡项,该法可令计算机直接输出任何级近似解的公式;