Abstract
For linear nonholonomic constraint systems, we prove that Jourdain's principle is not derived from D'Alembert's principle but equivalent to it if the variation is defined in the phase space rather than the configuration space. For nonlinear nonholonomic constraint systems, that the virtual displacements are undefined causes the inability of D'Alembert's principle to treat them; Jourdain's principle can be proved to be applicable through the application of Gauss's principle. The Newton-Euler equations of motion for rigid bodies in the form of Jourdain variational principle is first derived. The merit of Jourdain's principle relative to Gauss's principle is that the former does not need to evaluate the acceleration in the derivation of the equations of motion as does the latter.
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