For the behavior of polynomial roots in general, see Geometrical properties of polynomial roots.
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Spirule
In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This is a technique used as a stability criterion in the field of classical control theory developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot).
Evans also invented in 1948 an analog computer to compute root loci, called a "Spirule" (after "spiral" and "slide rule"); it found wide use before the advent of digital computers.[1][2][3][4][5][6][7][8][9]
^"1990". McKelvey School of Engineering at Washington University in St. Louis. Retrieved 2023-03-12.
^Evans, Walter R. (1965), Spirule Instructions, Whittier, CA: The Spirule Company
^Robert H., J.C. (2012). Dynamics of Physical Systems. Dover Civil and Mechanical Engineering. Dover Publications. p. 727. ISBN 978-0-486-13969-2. Retrieved 2023-03-12.
^Doebelin, E.O. (1985). Control System Principles and Design. Wiley. p. 312. ISBN 978-0-471-08815-8. Retrieved 2023-03-12.
^Savant, C.J. (1958). Basic Feedback Control System Design. Engineering special collection. McGraw-Hill. Retrieved 2023-03-12.
^Harris, L.D. (1961). Introduction to Feedback Systems. Wiley. ISBN 978-0-598-48455-0. Retrieved 2023-03-12.
^D'Azzo, J.J.; Houpis, C.H. (1968). Principles of Electrical Engineering: Electric Circuits, Electronics, Instrumentation, Energy Conversion, Control Systems, Computers. C. E. Merrill Publishing Company. Retrieved 2023-03-12.
^Gupta, S.C.; Hasdorff, L. (1983). Fundamentals of Automatic Control. Krieger. ISBN 978-0-89874-578-8. Retrieved 2023-03-12.
^Dransfield, P. (1968). Engineering Systems and Automatic Control. Prentice-Hall. Retrieved 2023-03-12.
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9. Sloan, M.C. (2010). "Aristotle's Nicomachean Ethics as the Original Locus for the Septem Circumstantiae". Classical Philology. 105 (3): 236–251. doi:10...
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