Analytical dynamics of continuous medium and its application

First, the studying progress of domestic and foreign scholars on analytical dynamics of continuum is reviewed. This paper mainly studies the problem of applying the Lagrange equation to the continuum dynamics. By using Lagrange-Hamilton system, Lagrange equations and their applications are investigated for non-conservative nonlinear elastic dynamics, incompressible viscous fluid dynamics, viscoelastic dynamics, thermal elastic dynamics, rigid-elastic coupling dynamics and rigid-liquid coupling dynamics. The establishment of finite element calculation model by using Lagrange equation was analyzed. Finally, the prospects of applying the Lagrange equation to problems of the continuum dynamics are discussed.