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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Volume were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(5), 940-945; doi:10.3390/mca15050940

Hard Fling Objector Contact with Surface of Fluid as a Ricochet

Measurement Institute, Henan Polytechnic University, 2001 Sijidadao, Jiaozuo, 4540001, China
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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For a hard flying objector contacts with the surface of fluid, there exists a critical contact angle between the flying direction and the surface direction. When the actual contact angle is less than the critical angle, the flying objector will get additional moment in flying direction and be rebounded up to tens grades. This critical angle is determined by the flying velocity and elastic constants of fluid. These phenomena are named as ricochet which essentially is due to the dynamic pressure of the fluid acting upwards on the flying objector to overcome its gravity force. Although the skipping of a flat stone on water surface is well known practices, the essential theoretic interpretation is not suitably formulated. In this research, it is shown that the fluid has two typical deformation modes: one is orthogonal rotational deformation (which is related with conventional contact), another is orthogonal rotation with intrinsic volume expansion. For the first kind of deformation, the dynamic pressure is inward direction, so the objector will sink into the fluid. However, for the second of deformation, the dynamic pressure is upward direction, so the flying objector will be raised up. It is this mechanism that produces the ricochet phenomenon. In this paper, the dynamic stress is determined by the fluid deformation. Then the contact condition equations are used to establish the related phenomenon. Based on these formulations, the critical angle is expressed by the flying velocity, mass and the fluid viscosity parameters. The related mechanic equations are formulated also. These results may promote the researches on the dynamic contact problem with bifurcation, such as ricochet and/or emerging.
Keywords: Critical angle; ricochet; dynamic contact; dynamic stress; local rotation; intrinsic strain; rational mechanics Critical angle; ricochet; dynamic contact; dynamic stress; local rotation; intrinsic strain; rational mechanics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Xiao, J.-H. Hard Fling Objector Contact with Surface of Fluid as a Ricochet. Math. Comput. Appl. 2010, 15, 940-945.

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