On the Geometry of Nonholonomic Dynamics

[+] Author and Article Information
H. Essén

Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

J. Appl. Mech 61(3), 689-694 (Sep 01, 1994) (6 pages) doi:10.1115/1.2901515 History: Received March 05, 1993; Revised May 26, 1993; Online March 31, 2008


The formulation and derivation of equations of motion for finite degree-of-freedom nonholonomic systems, is discussed. The starting point is Newton’s equation of motion in the 3K -dimensional unconstrained configuration space of K particles. Constraints represent knowledge that motion is only possible along some directions in the local tangent spaces. Only projections of the 3K -dimensional vector equation onto these allowed directions are of interest. The formalism is essentially that of Kane-Appell cast into an abstract form. It is shown to give the same equations as Hamel’s generalization of Lagrange’s method. The algorithmic advantage of the Kane-Appell projection approach is stressed.

Copyright © 1994 by The American Society of Mechanical Engineers
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