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Flight Simulation of Orbital and Reentry Vehicles Part I - Development of Equations of Motion in Six Degrees of Freedom

Report Number: ASD TR 61-171 Volume 1
Author(s): Gabriel Isakson
Corporate Author: University of Michigan
Laboratory: Behavioral Sciences Laboratory
Date of Publication: 1961-10
Pages: 41
Contract: AF 33(616)-5644
Project: 6114
Task: 611407
AD Number: AD0269282

Equations governing the motion of a lifting reentry vehicle in six degrees of freedom are developed for simulation purposes. Effects of earth rotation, earth oblateness and wind velocity are included. The rotational equations are conventional equations involving angular rates referred to body axes. Two different formulations of the translational equations are presented, using different coordinate systems. One involves spherical coordinates referred to the equatorial plane of the rotating earth; the oth r involves spherical coordinates referred to a nominal trajectory plane fixed with respect to inertial axes. The former has the advantage that earth rotation and oblateness are taken into account more simply, but an indeterminacy is encountered in the event of flight over a pole. The latter formulation eliminates this indeterminacy but is otherwise more complex. It is concluded that the equations developed are suitable for digital or hybrid analog-digital computation, but that accuracy requirements would be excessive for analog computation exclusively. An alternative formulation, suitable for analog computation, is presented in Part II of the present series (AD-269 283)

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