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The nonholonomic mapping put forward by Kleinert is generalized to a first-order linear mapping. By means of this method, Riemann-Cartan space is embedded into Euclidean space. Based on this construction, the d'Alembert-Lagrange principle of nonholonomic constrained systems in Euclidean space is reduced to an “unconstrained” representation on Riemann-Cartan space.
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