D'Alembert's principle is manipulated in the presence of nonholonomic constraints to derive the principle of virtual power in nonholonomic form, and Lagrange's equations for nonholonomic systems. The Lagrangian equations had been expressed previously for conservative systems, derived by variational methods. The D'Alembert derivation confirms the roles of constrained and unconstrained Lagrangians directly by the presence of constrained and unconstrained velocities in D'Alembert's principle. The constrained form of nonconservative generalized forces is also determined for both particles and rigid bodies. An example is a rolling disk.
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Design Engineering
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