## A Modified Quasilinearization Concept for Solving the Nonlinear Two-point Boundary Value Problem |

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AIAA Journal algebraic equations assumed terminal assumed value boundary value problem Breakwell Bryson ref classical optimality condition control variable convergence characteristics convergence envelope convergence sensitivity defined in equation Earth-Mars transfer envelopes for 20 equations of motion Euler-Lagrange variables gravitational constant independent variable initial conditions Initial iteration factor initial solution initial values initially assumed parameters iterative method Jazwinski ref Kenneth ref Lagrange multiplier Lewallen Manned Spacecraft linear differential equations linear Euler-Lagrange differential McGill and Kenneth Mclntyre ref method more competitive method proposed metric minimum-time Modified Generalized Newton Modified Quasilinearization Method Newton-Raphson Method nonlinear differential equations NONLINEAR TWO-POINT BOUNDARY nth trajectory previous nominal trajectory problem variables proposed quasilinearization methods radial Raphson Method required initially assumed SOLVING THE NONLINEAR Spacecraft Center spacecraft mass Speyer starting vector terminal boundary conditions terminal conditions terminal constraints terminal time determination terminal time error terminal value thrust direction relative tion total derivative Trajectory Optimization two-dimensional two-point boundary value vergence