A NONLINEAR NONHOLONOMIC FORMULATION OF THE APPELL-HAMEL PROBLEM

The Appell-Hamel non-holonomic problem which is intrinsically linear, has been formulated by the same authors as a non-linear problem by mea ns of a limiting procedure. This limiting process has been shown to be incorrect, in addition to being unnecessary in problems with rolling- type contact, where the constraint relations are known to be linear. I t is well established however, that there exist non-linear non-holonom ic constraints that arise from sources other than rolling-type contact . In order to be able to study the effect of constraints that arise fr om sources other than rolling, the Appell-Hamel problem is reformulate d in terms of nan-linear non-holonomic constraints, leading to the sam e results as the linear formulation, thus validating the non-linear an alysis. A complete set of constants of the motion are derived, and lim iting motions are investigated. The paper concludes with a description of the general method of solution to determine the time-history of th e generalized coordinates. It ends with a detailed discussion of the n umerical integration of the equations of motion. (C) 1997 Elsevier Sci ence Ltd.