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Dynamics of Impacts and Collisions of the Rolling Balls

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Book cover Dynamical Systems: Theoretical and Experimental Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 182))

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Abstract

In the chapter the theory of dynamics of impacts and collisions of the rolling balls is presented for different types of impacts and collisions depending on the balls’ configuration in the kinetic state of impacts and collisions. By use of analogy between central impacts or collisions of balls in translator motion and balls’ rolling motions before impacts or collisions, corresponding relations between outgoing velocities and outgoing angular velocities of rolling and impact velocities are expressed. Also, change of impact impulse (linear momentum) and moment of impulse (angular momentum) of the balls’ rolling motion after and before impacts and collisions are expressed. By use of phenomenological mappings between a set of element dynamics of balls’ impact and collisions for central and skew impacts as well as collisions corresponding analogies are identified. Different ball-rolling traces before and after skew impacts and skew collisions as a set of different kinematic elements for each type of impact and collision are discussed and kinematic plans of impacts and corresponding outgoing translator and angular velocities are graphically presented by a series of figures. In conclusion, dynamics of elliptic billiards are presented.

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Acknowledgments

Parts of this research were supported by the Ministry of Sciences of Republic Serbia through the Mathematical Institute SANU Belgrade Grant ON174001: “Dynamics of hybrid systems with complex structures; Mechanics of materials,” and Faculty of Mechanical Engineering, University of Niš.

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Authors and Affiliations

  1. Department of Mechanics, Mathematical Institute of Serbian Academy of Science and Arts (SANU), Knez Mihailova 26/III, Belgrde, Serbia

    Katica R. (Stevanović) Hedrih

  2. Faculty of Mechanical Engineering, University of Niš, ul Vojvode Tankosića 3/22, 18000, Niš, Serbia

    Katica R. (Stevanović) Hedrih

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  1. Katica R. (Stevanović) Hedrih
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Correspondence to Katica R. (Stevanović) Hedrih .

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Editors and Affiliations

  1. Dept. of Autom., Biomech. and Mechatr., Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

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(Stevanović) Hedrih, K.R. (2016). Dynamics of Impacts and Collisions of the Rolling Balls. In: Awrejcewicz, J. (eds) Dynamical Systems: Theoretical and Experimental Analysis. Springer Proceedings in Mathematics & Statistics, vol 182. Springer, Cham. https://doi.org/10.1007/978-3-319-42408-8_13

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