Decision Procedure ofMaximumLanding AreaApplied Homotopy Method
Seiya Ueno · 2006
Optimal control theory isapplied toalarge numberoftrajectory designs inaerospace engineering. For example, areusable spaceplane usesatrajectory toanorbit withminimumfuel oranon-powered aircraft isrequired to glide asfaraspossible. Optimal control theory provides thenecessary conditions ofoptimal trajectory. Theproblem is defined asantwo-point boundary value problem (TPBVP). There is, however, nosolution foraTPBVPinsomecases duetosevere terminal conditions. This paper discusses onprocedure tofind theexistence ofsolution inaTPBVPusing homotopy method. Homotopy method isanumerical calculation inwhichaguessed solution changes continually tothe exact solution withdefinite integration. There isnoassumption suchaslinearization, thus theexistence ofsolution is clearly showninthenumerical calculation andtheexact solution isprovide withfinite numbers ofcalculation. This paper isanintermediate report that theprocedure isapplied tothemaximumrange fornon-powered aircraft.