In order to solve the coexistence of catenary chain and ground chain in anchor chain multi-body system without adding the additional equations or judgment conditions, it is proposed to describe the state equation of static anchor chain multi-body system, namely the minimum potential energy equation, with the optimization principle, and the comparative analysis with the traditional catenary equation and general mechanical equation of multi-system is made. The results show that the method is simple in form and clear in physical meaning without the complicated force analysis. The numerical calculation results are consistent with the traditional method in the catenary calculation, and the coexistence of catenary chain and ground chain can be calculated under a unified framework.