Abstract: The nonlinear dynamic equation with two end faces in relativistic rotation is established, which contains a kind of nonlinear elastic force. The qualitative analysis of the relativistic rotational nonlinear autonomous equation is performed, and the stability of the equation is studied. The high-order approximate solution of the equation under forcing excitation is obtained by parameter transformation method.

Keywords: 
• relative rotation /
• nonlinear dynamics equation /
• nonlinear elastic coefficient /
• steadiness