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<title>AAS 98-132</title><body BGCOLOR="ffffff"> <h2>AAS 98-132</h2> <h2>EXACT ANALYTICAL SOLUTION TO A THREE-DIMENSIONAL INTERCEPTION OF A MANEUVERING TARGET</h2> <h4>N. X. Vinh, P. T. Kabamba, T. Takehira - The University of Michigan</h4> <h2> Abstract </h2> The 3-dimensional guidance problem has been extensively discussed in the open literature. However, because of the non-linearity of the equations of relative motion, its analytical solution is generally expressed in the form of non-integrable quadratures. In this paper, we generalize a guidance law, first studied by Cochran, to include a component of the relative commanded acceleration along the line-of-sight as well as its orthogonal component. For this more general guidance law, exact analytical solution to the 3-dimensional guidance problem is obtained explicitly in closed-form with two arbitrary control parameters. Application to the interception of a satellite in circular orbit is presented. <P><A HREF="http://www.space-flight.org/AAS_meetings/1998_winter/sessions.html">Back</A>