Analysis of junction points in optimal aeroassisted orbital plane change

摘要

The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. ^The problem formulation includes the thrust magnitude as a control variable. ^The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. ^An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. ^This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. ^The necessary conditions for the jump discontinuities in the angle of attack and thrust control are derived. ^We show that this set of necessary conditions permits a nontangential entry. ^One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points. ^(Author)