The motion equation of the particles is converted into 2nd order ordinary differential equation with a nonlinear term in the frame of classical physics. The solution of equation, and the oscillation period of particles are represented analytically by Jacobian elliptic function and the 1st kind of complete elliptic integral. Some important properties of the radiation are discussed, the maximum radiation energy for the position and the spectral distribution are calculated. The comparison shows essential agreement between the experiment and the theory.