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- W1946903312 abstract "The tangent-half-angle substitution is commonly used to convert “goniometric” equations in the sine and cosine of a certain variable θ into polynomial equations in a new variable x= tan(θ/2). This facilitates the solution of goniometric equations and systems of equations. Elementary problems concerning the special case tan(±π/2) and the introduction of trivial extraneous roots into systems of equations are well known and can be handled. The article shows that nontrivial extraneous roots may be generated when a tangent-half-angle substitution for some variable is used to derive a characteristic equation for another vari able from a goniometric system of equations. An effective method is presented to decide before the symbolic solution of a system whether a tangent-half-angle substitution produces such extraneous roots. The results can also be used to detect relevant simple subclasses of manipulators in a given superclass when no general symbolic solution for the superclass is explicitly known. As an application, it is proven that the Raghavan-Roth algorithm for the symbolic solution of the inverse kinematics problem never generates these nontrivial extraneous roots." @default.
- W1946903312 created "2016-06-24" @default.
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- W1946903312 date "1993-01-01" @default.
- W1946903312 modified "2023-10-03" @default.
- W1946903312 title "On the Tangent-Half-Angle Substitution" @default.
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- W1946903312 doi "https://doi.org/10.1007/978-94-015-8192-9_3" @default.
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