On the governing equations of motion of nonholonomic systems on Riemannian manifolds
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We propose a geometric approach to formulate the governing equations of motion for a class of nonholonomic systems on Riemannian manifolds. We first present a coordinate-free geometric formulation of the D’Alembert–Lagrange equation. Then by explicating this geometric formulation with respect to an arbitrary frame, we obtain the governing equations of motion in generalized form. The governing equations so obtained directly eliminate the dependent variations without using undetermined multipliers. As examples, we apply the formulation to a rigid body and a system with general first-order nonholonomic constraints; we also demonstrate their equivalences to the known results.
KeywordsRiemannian Manifold Lagrange Equation Virtual Work Cotangent Bundle Geometric Formulation
- 4.Kane, T. R. and Levinson, D. A., Dynamics: Theory and Applications, McGraw Hill, New York (1985).Google Scholar
- 8.Mei F. X., Foundations of Nonholonomic Mechanics (In Chinese), Beijing Institute of Technology Press, China (1985).Google Scholar
- 9.Niemark J. I. and Fufaev, N. A., Dynamics of Nonholonomic Systems, American Mathematical Society, Providence, RI (1972).Google Scholar