Advances on the Simplification of Sine–Cosine Equations

✍ Scribed by Jaime Gutierrez; Tomas Recio

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 725 KB
• Volume: 26
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1998.0200

✦ Synopsis

In this paper we contribute several results to the approach initiated by Hommel and Kovács (well documented with applications in a recent book by Kovács (1993)) on the symbolic simplification of sine-cosine polynomials that arise, for instance, as determining equations for joint values in robotics inverse kinematic problems. We present, taking into consideration for the first time sine-cosine polyomials, fast algorithms for the functional decomposition and factorization problems, reducing the solving of such s-c equations to a sequence of lower degree ones. Moreover, we show that triangularization of a given sine-cosine equation provides a conceptual understanding of the conditions that yield extraneous roots in the half-angle tangent substitution (and therefore that imply a reduction of the degree in the determining equation of a given s-c system).