中文摘要：

Appell方程是分析力学中的一类重要方程,该方程既可以用来描述完整系统又可以用来描述非完整系统.通过将Appell方程表示为广义梯度形式,进而可以借助梯度系统的某些性质来研究Appell方程的解及其稳定性问题.为此,本文先将梯度系统推广为包含时间变量的广义梯度系统,再给出Appell方程可化为广义梯度系统的条件,最后利用广义梯度系统的性质来研究Appell方程解的稳定性问题,并结合实际例子说明理论的应用.

英文摘要：

Appell equation is a kind of important equations in analytic mechanics,which is not only suitable for holonomic systems but also applicable to nonholonomic systems.In order to study the stability of solutions of Appell equations,the gradient systems were extended to generalize gradient systems which contain the variable of time.Two kinds of generalized gradient systems were put forward and the characteristics of the systems were studied.The conditions under which Appell equations could be considered as one of two generalized gradient systems were obtained.Then,the stability of solutions of Appell equations were studied based on the characteristics of generalized gradient systems.Some application results show the feasibility.