Graduate Thesis Or Dissertation

 

Predicting rebound of planar elastic collisions Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/qz20sv620

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  • Impact is a large and complex field. It embraces both structures as simple as a nail, and more complex systems, such as a car collision. A central feature of impact theory is finding the dependence between the velocities before and after impact. The transformation law of the velocities in an impact interaction can be represented in a purely geometric form, and therefore in the simplest cases, in describing the motion of systems with impacts, it is possible to get by with entirely elementary tools. However, in most engineering applications, the mechanical interactions occurring during a collision are complex. Therefore, impact is usually described by highly complicated mathematical models that can easily lead to cumbersome intricacies. Hitherto, the theories that have been developed either involve a fairly heavy amount of calculations or are severely oversimplified, and, therefore, limited in their application. Our purpose is first to describe the dynamics of a planar collision with as simple equations as possible, and secondly to extract information from those equations with the least and simplest computation. We achieve our task by combining a Kane's dynamical analysis, a simplified model of the deformation of the contact area during impact, and a numerical integration of a set of ordinary differential equations. Subsequently, we verify the consistency, accuracy and efficiency of our results by comparison to those from earlier theories.
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