Finite and impulsive motion of constrained mechanical systems via Jourdain's principle: discrete and hybrid parameter models |
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Authors: | József Kövecses William L Cleghorn |
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Institution: | a John H. Chapman Space Centre, Canadian Space Agency, 6767 route de l'Aéroport, Saint-Hubert, Québec, Canada J3Y 8Y9 b Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd., Toronto, Ont., Canada M5S 3G8 |
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Abstract: | The main purpose of this paper is to present a unified analytical dynamics framework for the analysis of finite and impulsive motion of mechanical systems using Jourdain's principle. Emphasis is given to the general case when a mechanical system is described by a hybrid (discrete-distributed) parameter model. A large group of finite and impulsive, generally non-holonomic, constraints are analysed in detail and a so-called extended Appellian classification is presented for these constrained motion problems. The fundamental dynamic equation of constrained systems is developed in terms of velocity variations (Jourdain's principle). Based on this equation and the constraints, the methods of quasivelocities and Lagrangian multipliers are adopted and interpreted for the finite motion of hybrid parameter models of mechanical systems; and the methods of independent quasivelocity variations and Lagrangian multipliers are introduced for the analysis of impulsive motion of such models. To illustrate the proposed material, an example of a one-link flexible arm intercepting and capturing a moving target is considered. |
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Keywords: | Analytical dynamics Constraints Impulsive motion Jourdain's principle Equations of motion |
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