In order to solve the problem of optimal impulsive orbital 3D maneuver with or without time constraint one must first solve theoptimal condition's equations. There are different and numerous modes of geometry, all of these modes must be considered.Solving this problem with the geometric modes has, to my knowledge, not been done before. In this paper the problem has beensolved in two states: with time constraint and no time constraint while considering all possible geometric modes. The purpose ofthis paper is solving the problem and achieving the global solution. For considering all possible modes of geometry, the relations ofoblique spherical triangle must be used. All necessary angles can be determined by using these relations. In this paper, 16 modes forexposure of initial orbit to final orbit and 16 modes for exposure of transfer orbit to initial and final orbits are classified. Then, theoptimal condition equations have been solved. Solving the equations led to only one local minimum and the global solution cannotbe identified. Therefore, the process is required to determine global solution. In this paper, the explicit equations have beenextracted which by using them, intermediary variables evaluated with respect to independent variables. Then, the function ofimpulse can be minimized to independent variables separately. The exact location of global solution can be determined byexamining the behavior of the function to the independent variables. Therefore, the global solution can be obtained. Finally, themethod is applied for the numerical example. The initial and final orbits is elliptical and non coplanar and elements of them arecertain. The example is solved in two modes of time constraint and no time constraint. In time constraint mode, the time of transfermust be 2500 seconds. In this mode some results have been verified by solving the Lambert problem. In the non time constraintmode, the total required impulse is less than the time constraint mode as expected. The solutions of two of these modes have beensimulated by MATLAB code. The results show acceptable accuracy and high-speed computing.
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