Numerical Continuation of Aeroelastic Systems: Shooting vs Finite Difference Approach

Nonlinearity in aeroelastic systems has become an important area of research. It is widely recognised that
nonlinearities due to the structure, control system or aerodynamic forces can affect aeroelastic systems,
such as aircraft, and can cause oscillatory phenomena that cannot be predicted using a purely linear
analysis. An important class of methods for predicting such phenomena from the equations of motion of a
nonlinear aeroelastic system is numerical continuation. There are several techniques for the application
of numerical continuation, each with its advantages and disadvantages. Here, the finite differences and
shooting approaches are implemented and compared. Both approaches are applied to a simple pitchplunge
nonlinear aeroelastic mathematical system.