Use of Quaternions in Flight Mechanics
Abstract
In analyzing aircraft spin and other flight maneuvers with large rotation rates based upon first principles, the non-linear aerodynamic equations (Navier-Stokes) must be coupled with the rigid-body dynamic equations of motion. In both systems of equations it is desirable to use a body axes system to describe the forces and moments, and utilize a surface-oriented coordinate system for obtaining the flowfield grid. To solve this system of equations it is necessary to describe the position of the aircraft with respect to a fixed inertial coordinate system. The classic method is to use the Euler angles to define the aircraft orientation. However, singularities and ambiguities exist when the elevation angle is plus or minus ninety degrees. This difficulty has been overcome in the field of inertial guidance by the use of quaternions to describe the aircraft position in space. It is the purpose of this report to investigate this technique for numerically solving aircraft spin problems. Two problems are addressed; the first is a nonsymmetric body and the second is a symmetric configuration. The rotational dynamics and the solution for the quaternions and Euler angles are determined for both problems. Hamilton (circa 1840) was the first to point out that the three Euler angles are inadequate to uniquely define the orientation of a body in space and that four variables are required to resolve the predicament. Hence he invented the quaternion which is a scalar plus a vector, totalling four elements.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1984
- Accession Number
- ADA152616
Entities
People
- L. E. Miller
- S. J. Scherr
- W. L. Hankey
Organizations
- Wright Laboratory