Point-connected rigid bodies in a topological tree |
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| Authors: | Peter W Likins |
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| Institution: | 1. School of Engineering and Applied Science, University of California, Los Angeles, Calif., USA
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| Abstract: | Identical equations of motion are shown to emerge for a system ofn+1 rigid bodies all interconnected byn points, each of which is common to two bodies, by means of each of the following derivation procedures, all of which employ a kinematical identity developed by Hooker and Margulies: The Hooker-Margulies/Hooker equations; Kane's quasicoordinate formulation of D'Alembert's principle; the combination of Lagrange's generalized coordinate equations and Lagrange's quasicoordinate equations; and the combination of Lagrange's generalized coordinate equations and the vector rotational equationM=H applied to the total system and resolved into a vector basis fixed in a reference body of the system. Thus the previously published Hooker-Margulies/Hooker equations are shown to be the natural result of several derivation procedures other than the Newton-Euler method originally used, provided that the central kinematical identity of the original derivation of Hooker and Margulies is employed. |
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