Design ForumDESIGN FORUM papers range from design case studies to presentations of new methodologies to speculations about emerging design trends. They vary from 2500 to 12,000 words (where a figure or table counts as 200 words). Following informal review by the Editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover). Tools based on the bifurcation and continuation method have been found to be extremely useful for studying multiparameter nonlinear dynamical systems under state and parameter-constrained conditions. Because of inherent limitations of the existing methodologies, however, application of continuation techniques to certain types of problems has remained cumbersome and even computationally challenging. This paper provides an alternate direct approach in MATLAB ® using its continuation subroutine MATCONT to extend the capabilities of continuation techniques in an attempt to accommodate a wide variety of constrained dynamics problems. Published results in the literature are first reproduced for validation of the proposed approach. A control problem of scheduling gains for the longitudinal flight dynamics of an aircraft is next presented to show usefulness of the proposed methodology, followed by solutions to an aircraft conceptual design problem involving wing morphing with eigenvalue constraints, with the difficulties of the selected problems increasing in that order.
Direct
Nomenclature b= wing span, m C D , C L , C Y = coefficients of drag, lift, and side force, respectively C l , C m , C n = aerodynamic rolling, pitching, and yawing moment coefficients, respectively c = mean aerodynamic chord, m I x , I y , I z = roll, pitch, and yaw moments of inertia, kg ⋅ m 2 Ma = Mach number m = mass of aircraft, kg p, q, r = body axis roll, pitch, and yaw rates, respectively, deg ∕s S = wing planform area, m 2 T m = maximum available engine thrust, N V = velocity of aircraft, m∕s α, β = angle of attack and sideslip angle, respectively, deg δe; δa; δr = elevator, aileron, and rudder deflection angles, respectively, deg η = thrust as fraction of maximum available thrust μ, γ = wind-axis angles, deg ρ = air density, kg∕m 3 ϕ, θ = Euler bank and pitch angles, respectively, deg