Dynamic Stability Analysis of Blunt-Body Entry Vehicles Using Time-Lagged Aftbody Pitching Moments

Abstract

This analysis defines an analytic model for the pitching motion of blunt bodies during atmospheric entry. The proposed model is independent of the pitch-damping sum coefficient present in the standard formulation of the equations of motion describing pitch oscillations of a decelerating blunt body, instead using the principle of a time-lagged aftbody moment as the forcing function for oscillation divergence. It is shown that the dynamic oscillation responses typical to blunt bodies can be produced using hysteresis of the aftbody moment in place of the pitch-damping coefficient. Four parameters, all with intuitive physical relevance, are introduced to fully define the aftbody moment and the associated time delay. The approach used in this investigation is shown to be useful in understanding the governing physical mechanisms for blunt-body dynamic stability and in guiding vehicle and mission design requirements. A validation case study using simulated ballistic range test data is conducted. From this, parameter identification is carried out through the use of a least-squares optimizing routine. Results show good agreement with the limited existing literature for the parameters identified, suggesting that the model proposed could be validated by a limited experimental ballistic range test series or with existing data. The trajectories produced by the identified parameters are found to match closely those from the Mars Exploration Rover ballistic range tests for a range of initial conditions.

Additional Information

This work was supported by a NASA Space Technology Research Fellowship. Cole Kazemba is incredibly grateful for the invaluable advice and support from Milad Mahzari, Soumyo Dutta, Chris Cordell, and the rest of the Georgia Institute of Technology Space Systems Design Laboratory.

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