The purpose of this paper is to establish a set of numerical methods to determine, according to the given helicopter geometrical configuration parameters, helicopter nonlinear mathematical models which are required in the simulations and control for helicopter motion. The approach starts with the theories of flight dynamics and aerodynamics to establish the nonlinear mathematical model of helicopter Then, by using the equilibrium of force and moment, the trim points of different flight conditions of the helicopter are determined. At each trim point, the linearized model is derived by using the Taylor's series expansion, based on which poles (eigenvalues) can be found and stability analysis can be conducted. Finally, various control laws are added to the established mathematical model and nonlinear simulations are employed to verify the helicopter motions.