Abstract: It is very difficult to obtain an exact analytical solution to a nonlinear ordinary differential equation, so till now analytical solutions are rare in this area. The author has obtained the exact analytical solutions of this type of nonlinear oscillations. In this paper as an example, the exact analytical solution of nonlinear oscillation of a two-dimen-sional lift body, which has attracted the attention of research workers for a long time, is given.

Key words: exact Cosserat model, Kirchhoff’s rod, Lyapunov’s stability, Euler’s load