关于非线性机床再生颤振的Hopf分支

ON THE HOPF BIFURCATION OF THE NONLINEAR REGENERATIVE TREMOR OF A MACHINETOOL

本文讨论机床再生颤振的方程变形后的方程在参数空间(a,b,c)中周期分支的情况.给出分支曲面的轮廓,还给出在原点邻域内周期解和周期的近似表达式.

In this paper, the equationis discussed, this equation is the another form of the tremor equation of the machine toolis discussed. The periodic bifurcation in the parametric space (a, b, c) is considered (all the cocfficients are nonncgative.and b>c.).The sketch of the periodically bifurcat surface in the parametric space (a,b,c) and the locally approximate expressions of the periodic solution and its period in the neighbourhood of the original point are given.