Space trajectory computation at the University of Michigan

Abstract

Extensive investigation of methods of real-time and fast- time computation of earth orbits and reentry trajectories has been conducted for both analog and digital computers. Integrator drift and multiplier errors in the case of analog computers preclude the use of direct computation in in ertial frames or geocentric coordinate systems. Such co ordinate systems can also lead to serious digital computer problems due to truncation and roundoff errors. Introduc tion of a vehicle-centered rotating coordinate system with variables referred to a nominal orbit permits greatly im proved computer scaling which, in turn, very substantially improves the absolute computational errors. In addition, the use of angular momentum and energy constraints is shown to reduce greatly the effect of integrator drift on the in-plane motion. Analog solutions to orbital and re entry problems have been obtained in real-time, fast-time, and high-speed repetitive operation using the above co ordinate system.

Constraint violation stabilization using gradient feedback in constrained dynamics simulation

“…16 The correction forces are applied to the equations of motion so that the integration of q and q moves in the direction that most rapidly reduces the violation of the energy constraint. 17 To ensure that the minimum 17 ' 18 of ^ is zero, the negative gradient of ^2 is fed back into the equation of motion (8). That is,…”

Hybrid Computer Methods for Direct Functional Optimization

“…Recently, so-called direct approaches to func tional optimization on hybrid computers have been inves tigated by Fogarty and Howe (1968). By using a high-speed hybrid computing system, one is able to compute all of the needed gradients simultaneously, as the response to small "impulsive" control perturbations.…”