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A non-linear non-holonomic formulation of the Appell-Hamel problem
Journal article   Peer reviewed

A non-linear non-holonomic formulation of the Appell-Hamel problem

Leon Y. Bahar
International journal of non-linear mechanics, v 33(1), pp 67-83
1998
DOI: https://doi.org/10.1016/S0020-7462(96)00148-5

Abstract

Appell-Hamel problem constrained dynamics non-linear non-holonomic systems
The Appell-Hamel non-holonomic problem which is intrinsically linear, has been formulated by the same authors as a non-linear problem by means 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. It is well established however, that there exist non-linear non-holonomic constraints that arise from sources other than rolling-type contact. In order to be able to study the effect of constraints that arise from sources other than rolling, the Appell-Hamel problem is reformulated in terms of non-linear non-holonomic constraints, leading to the same results as the linear formulation, thus validating the non-linear analysis. A complete set of constants of the motion are derived, and limiting motions are investigated. The paper concludes with a description of the general method of solution to determine the time-history of the generalized coordinates. It ends with a detailed discussion of the numerical integration of the equations of motion.

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