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Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion by J. Janová; J. Musilová is a Engineering article available to read on EtoBox.

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In the presented paper, a problem of non-holonomic constrained mechanical systems is treated. New methods in non-holonomic mechanics are applied to a problem of a general coupled rolling motion. Two goals are stressed. The first of them lies in the solution of an originally formulated problem of rolling motion of two rigid cylindrical bodies in the homogeneous gravitational field leading typically to non-linear equations of motion. A solid cylinder can roll inside a ring under the static frictional force assuring rolling without slipping, the ring rolls again without slipping along a generally shaped terrain formed by hills and valleys. "Surprising behaviour" of the mechanical system which permits interesting applications is studied and discussed. The second purpose of the paper is to show that the geometrical theory of non-holonomic constrained systems on fibered manifolds proposed and developed in the last decade by Krupková and others is an effective tool for solving non-holonomic mechanical problems. A comparison of this method to alternative methods is given and the benefits of coordinate-free formulation are mentioned. In this paper, the geometrical theory is applied to the a

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Author

J. Janová; J. Musilová

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0020-7462)

Published

2009

Field

Engineering (Physical Sciences)