Performance and Stability Analysis of the Non-Linear Dynamics of a Simple Powered Lifting Hypersonic Vehicle Flying on a Minor Circle

Date of Award

12-1991

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Aeronautics and Astronautics

Abstract

The nonlinear equations of motion for a hypersonic vehicle flying on a minor circle were modeled using the control design and simulation software package, MATRIXx. The model includes earth rotation and gravity gradient effects. Aerodynamic forces and moments are expressed as first order Taylor series expansions using the full nonlinear expression for the dynamic pressure. Minor circle equilibrium flight conditions are generated via a Newton iteration technique (Turbo Pascal program) for both a rotating and non-rotating earth model. Equilibrium performance over speeds from Mach 5 to Mach 40 and 0 to 85 degree latitudes at east and west flight headings are compared. The speed and latitude determine equilibrium bank angles, altitude, and roll, pitch, yaw control moments (to sustain minor circle flight). These parameters are analyzed to assess equilibrium performance. Results show that earth rotation and gravity gradient torques have significant effects on performance. The system is shown (via MATRIXx) to be marginally unstable. For near-major circle routes, the modes are poorly damped and decoupled into lateral and longitudinal modes. For mid-latitude minor circle routes, the modes are poorly damped and coupled. However, the modes are comprised of either mostly longitudinal or mostly lateral states. For minor circle latitudes greater than 65 deg, we see poorly damped coupled modes, with new mode shapes appearing as equilibrium speeds increase.

AFIT Designator

AFIT-GA-ENY-91D-11

DTIC Accession Number

ADA243933

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