The solving of non?conservative and non?linear mathews?Lakshmanan oscillator is taken as an example to illustrate the application of the theories and methods of analytical mechanics in studying the non?linear systems.According to the theories of inverse problem of variational calculus, the equation of M?L oscillator is transformed into a self?adjoint equation. The Lagrangian and Hamiltonian of M?L oscillator are also constructed by four methods. Eventually, the equation of M?L oscillator is solved based on the Noether theory and the Hamilton?Jacobi method, respectively．