The derivation, solution, and analysis of airplane spin equations modeled in an inertial coordinate system

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Author
Buehler, Roy Robert
Date
1972-03Advisor
Schmidt, Louis V.
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Show full item recordAbstract
The general equations of motion for a rigid body are
derived in cylindrical coordinates by Lagrangian dynamics
and used to model the motion of an airplane in a steady spin.
After simplification, the equations are cast into a form
utilizing conventional aerodynamic derivatives along with
other derivatives which may be significant in spins. An
iterative numerical solution procedure is outlined which
should simplify the problem of solving the nonlinear differential
equations, and relationships between the Euler
Angles used in the equations and the more familiar ordered
set of pitch, roll, and yaw are derived to permit computer
input and output of orientation to be more easily visualized.
The inverse problem is also considered , and equations are
derived to translate spin test data into the six Lagrange
coordinates used so that computer calculations may be checked
against test results and actual aerodynamic forces can be
compared with computed values. The paper concludes with a
discussion of the implications of this spin analysis along
with applications and extensions.
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