The HIRM+ Flight Dynamics Model

The major objective of the GARTEUR Action Group on Analysis Techniques for Clearance of Flight Control Laws FM(AG-11) is the improvement of the flight clearance process by increased automation of the tools used for modelbased analysis of the aircraft’s dynamical behaviour. What is finally needed are techniques for faster detection of the worst case combination of parameter values and manoeuvre cases, from which the flight clearance restrictions are be derived. The basis for such an analysis are accurate mathematical models of the controlled aircraft. In this chapter the HIRM+ flight dynamics model is described as one of the benchmark military aircraft models used within FM(AG-11). HIRM+ originates from the HIRM (High Incidence Research Model) developed within the GARTEUR Action Group on Robust Flight Control M(AG-08). In building the HIRM+, additional emphasis has been put on realistic modelling of parametric uncertainties

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach