The Lagrangians and Hamiltonians of damped coupled vibrations

In this paper,the analytical mechanization of two kinds of damped coupled vibrations is studied. First,by use of coordinate transformations the equations of motion are transformed into the self-adjoint form.Secondly,the Lagrangians are obtained according to Engels method.Finally the Lagrangians and Hamiltonians of the original equations are deduced by using the inverse transformation.