为了解决工程实际中材料质量不均匀分布对双摆系统运动的影响，在均质物理双摆模型的基础上，将摆的质心位置和摆的转动惯量提取为变量，建立非均质双摆模型。将非均质双摆系统由Hamilton系统近似为拟Hamilton系统，运用双自由度的Melnikov法，得到拟Hamilton系统存在Smale马蹄意义下混沌的能量阈值，以此作为Hamilton系统的混沌条件。利用最大Lyapunov指数图、分岔图、Poincaré截面图等数值方法验证混沌条件的正确性，并详细分析了各参数对系统运动状态的影响和作用机制。结果表明，非均质双摆的混沌阈值有较高复杂性，而且摆长、摆重、第一摆的质心位置同时影响着系统的能量与混沌阈值，解释了质心位置和转动惯量等参数发生变化时，系统在混沌和拟周期之间交替变换的原因。进一步研究了参数取值与Melnikov法适用性之间的关系，通过数值仿真分类讨论了Melnikov法不适用时的参数取值情况。

In order to solve the influence of materials with uneven mass distribution on the motion of double pendulum system in engineering practice, a heterogeneous double pendulum model was established based on the homogeneous physical double pendulum model, in which the position of the center of mass and the moment of inertia of the pendulum were extracted as variables. In order to further explore the chaotic characteristics of the system, the heterogeneous double pendulum system is approximated from Hamilton system to quasi-Hamilton system, and the dynamics equation of the double pendulum system is obtained by using Euler-Lagrange equation of the second kind. The energy threshold of Smale horseshoe chaos in quasi-Hamiltonian system is obtained by using Melnikov method with two degrees of freedom, which is used as chaos condition of Hamiltonian system. After programming with Matlab, the correctness of chaos condition is verified by numerical methods such as maximum Lyapunov exponential diagram, bifurcation diagram and Poincare section diagram, and the influence of each parameter on the system motion state and action mechanism are analyzed in detail. The results show that the chaos threshold of heterogeneous double pendulums depends on many factors, including the initial energy of the double pendulums, the position of the center of mass of the first pendulums and the ratio of moment of inertia of the two pendulums. With the different values of each parameter, the system will change from the regular motion state with chaos threshold to the irregular and complex motion state without chaos threshold. The reason why the system alternates between chaotic state and quasi-periodic state is explained and the correctness of theoretical prediction is proved. When the center of mass of the first pendulum, the mass ratio of the two pendulums and the ratio of moment of inertia of the two pendulums are set to the limit values, the reasons for the difference between the theoretical threshold and the actual numerical simulation results are found and explained. On this basis, the relationship between parameter values and the applicability of Melnikov method is further discussed, and the parameters under which Melnikov method is no longer applicable are discussed by numerical simulation classification.