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Restricted maximum principles for elastic bodies

A maximum principle for the equilibrium of an elastic material body which is free of body forces is described not all of the components of the displacement vector or of the principal stresses can simultaneously have a strict maximum or minimum at any point in the body which does not be either on the surface or on a material interface.

Rose, M. E.

Maximum principle solutions for time-optimal half-loop maneuvers of a high alpha fighter aircraft

An investigation was conducted of maximum principle solutions for an initial 0.6 Mach number and 15,000-ft altitude. The authors generate these solutions for a family of prescribed final times tf, starting with tf = 0.5 s. Using a nonlinear wind-tunnel model they construct maximum principle solutions. Above tf = 1.2 s some small nonlinear variations in the aerodynamic pitching moment coefficient presented difficulty with respect to numerical convergence. This was circumvented by fitting analytical models to the aerodynamic coefficients of the wind-tunnel model at Mach 0.4. Maximum principle solutions of the analytical model are shown to compare well with those obtained for tf of less than 1.2 s. Using the analytical model the authors extended the prescribed final time to a value of 13.65 s at which time the aircraft completes the half-loop maneuver. This is 0.53 s longer than that obtained using the singular perturbation feedback control law.

Stalford, Harold

A maximum principle re-entry study

Mathematical model of maximum principle of Pontryagin used to find point-to-point reentry trajectory of space vehicle

REENTRY TRAJECTORY