*Brian F. Doolin*

*naca-tn-3968*

*May 1957*

The purpose of this paper is to show the method and advantages of matrix algebra in setting up the geometric aspects of problems of airplane motion. Such aspects arise particularly when studies of systems which include aircraft are being made. The geometry is formulated by fixing quantities whose relative motions are to be studied, each in a coordinate system of its own. The various coordinate systems are related to each other by orthogonal transformations in matrix form, and the parameters defining the transformations are found in terms of the dynamical variables of the problem with the help of the transformation matrices. The compact notation of matrix algebra permits a clear view of the geometry involved. Use of matrix algebra provides a routine procedure for computing the detailed expressions required in a particular problem. The first part of the paper discusses those aspects of matrix algebra required for use in orthoonal transformations. The second part shows how to use orthogonal transformations in matrix form by applying them in several examples.

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http://naca.central.cranfield.ac.uk/reports/1957/naca-tn-3968.pdf