In a mathematical context, the trajectory optimization problem is a nonlinear, multi-point boundary-value problem requiring a numerical solution. This solution is best obtained by the intensive, iterative calculations of a high-speed digital computer.

The good news is that there are several viable methods that can be programmed on a computer to obtain solutions.  Usually, a truly optimum solution is not cost-effective, and the engineer or scientist must be satisfied with a quasi-optimum solution. However, a thoughtful construction of the trajectory-optimization problem will usually result in a quasi-optimum solution that is not significantly different from the truly optimum solution.

A method I developed in the 1970's, and used successsfully for many years after that, is based on the iterative solution to a cleverly-constrained linear approximation of the non-linear optimization problem.  On each iterate, the Simplex algorithm (of linear programming) is used to solve the linear approximation.  The user defines the cost function and constraint equations and inequalities, and he also characterizes the control functions in terms of parameters (constants) whose optimum values are to be determined.

In practice, this adaptation of the Simplex algorithm has proven to be a robust, effective method for obtaining quasi-optimum solutions for a wide variety of missions involving rockets.  Over the years, the method has been enhanced as it has been applied to more and more mission types, involving different objectives and constraints.  What has been learned has, in large part, been incorporated into the first edition of a program named ZOOM.    This first edition is termed the "conceptual design and analysis" edition because the propulsion and aerodynamic models are relatively simple.  However, it can be a very useful tool to an aerospace engineer in trajectory shaping and rocket sizing tasks.

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