Abstract: Non-conservative nonlinear rigid-elastic-liquid-control coupling analytical dynamics is one of the important research subjects related to aerospace dynamics and multi-body dynamics. It is of great theoretical significance and practical value to study this theoretical and applied subject by using analytical dynamics method. Firstly, the non-conservative nonlinear Hamilton-type quasi-variational principle of rigid-elastic-liquid-control coupling dynamics with two types of variables is established. Based on the functional of the Hamilton-type quasi-variational principle with two types of variables, the characteristics of rigid-elastic coupling, rigid-liquid coupling, elastic-liquid coupling and rigid-control coupling are analyzed. Secondly, with the help of Lagrange-Hamilton system, the Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is derived from Hamilton-type quasi-variational principle. Thirdly, the governing equations of the non-conservative nonlinear rigid-elastic-liquid-control coupling system are derived by applying the Lagrange equations. Based on the governing equations, the mechanisms of rigid-elastic coupling, rigid-liquid coupling , elastic-liquid coupling and rigid-control coupling are analyzed. The application of Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is studied in two aspects. On the one hand, the finite element model is established by applying the Lagrange equations. Furthermore, the advantages of this kind of computing model are analyzed. On the other hand, the problems are analyzed by using the governing equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system. It illustrates the complementary characteristics of the application of analytic analysis and discussion to the study of problems and the application of numerical and quantitative analysis methods to the study of problems. Finally, several related issues are discussed.