A systematic technique is outlined that transforms linear state-space matrix equations in physical coordinates to a set of matrix equations in scaled, normalized, modal coordinates. Once the transformation to normalized modal coordinates is made, a series of techniques are defined to analyze: the fundamental modes of motion of the system; the impacts of the system inputs on these modes; and the appearance of these modes in the system outputs. A technique is also defined which uses the normalized modal matrices to compute a steady-state input vector which optimizes the steady-state response of selected system outputs. Graphics which promote quick understanding of the analysis are presented to display the resulting
vectors and matrices. The defined analysis techniques are applied to two example aerospace vehicle models. The results of these example applications illustrate the understanding which can be acquired using the described modal analysis techniques.
Note: Doug Arbuckle was my colleague at NASA and I supervised this/his Master’s Thesis project. Doug started as my co-op student, but shortly after I left in NASA he became one of the youngest-ever SES leaders at NASA-Langley. He now is an executive with the FAA.
“A teacher is well served by a student who exceeds him.” — Chinese proverb
Link to Master’s Thesis: link