Under classical mechanics,the general equation of particle motion in the periodic field is derived.In the dampless case,the existence possibility of the higher-order harmonic radiation is explored by using Bessel function expansion of a generalized trigonometrical function and the multi-scale method.In the damping case,the critical properties and a chaotic behavior are discussed by the Melnikov method.The results show that the use of a higher-order harmonic radiation of non-relativistic particle...