摘要
In practice,almost all real engineering systems are essentially nonlinear.Linear systems are just idealized models that approximate the nonlinear systems in a prescribed situation subject to a certain accuracy.Once nonlinearity is included,analytical solutions are rarely available for almost all real problems.Therefore,nonlinear computational methods are becoming important.In most aerospace problems,however,a relatively high-fidelity nonlinear model has to be established,especially when the system is immersing in a complicated environment and nonlinearity is not negligible anymore.Many complex phenomena,i.e.,bifurcation,limit cycle oscillation,chaos,turbulence,may occur in a variety of aerospace systems,which may be described by nonlinear Ordinary Differential Equations(ODEs)for rigid body problems or Partial Differential Equations(PDEs)for flexible solids or fluid mechanics problems.In general,nonlinearity in aerospace systems is often regarded as unwanted and troublemaker,due to the fact that considering nonlinearity makes the solution methods as well as the control methods more difficult.Therefore,there has been a general tendency to circumvent,design around them,control them,or simply ignore them.
