Optimal trajectories for maximum endurance gliding in a horizontal plane

Nomenclature C0,C/,C2,Cj = constants of integration CD = drag coefficient CDO =zero lift drag coefficient CL = lift coefficient CL* = lift coefficient for maximum lift-to-drag ratio D = drag force E* = maximum lift-to-drag ratio h = altitude H =Hamiltonian function kj,k2,k3 =constants, =C//C0, C2/C0, C3/C0, respectively K = induced drag factor L =lift force m =mass of the vehicle Px>Py>Pu>Pt>Pe = adjoint variables associated with state variables r — radius of penetration 5 = reference area / =time u = dimensionless speed V — speed of vehicle W — weight of vehicle x,y = dimensionless coordinates X,Y = position coordinates of vehicle A =tan/>t 0 = dimensionless time X = normalized lift coefficient jn =bank angle p = density of atmosphere T = normalized time 0 = velocity yaw angle co = dimensionless wing loading