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values and the applicability of Melnikov method is further discussed, and the parameters under which Melnikov method is no longer applicable are discussed by numerical simulation classification.