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Equations for Bat-Ball Collisions

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Abstract

Chapter 3 begins the mathematical analysis of bat-ball collisions. For collision at the center of mass of the bat, it presents equations for the Conservation of Linear Momentum, the definition of the Coefficient of Restitution and the Conservation of Energy. For collisions at the sweet spot of the bat, it adds Newton’s Second Principle, Impulse and Momentum. It introduces a uniform notation that will be used throughout the book, without jargon.

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References

  • Bahill, A.T.: The ideal moment of inertia for a baseball or softball bat. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 34(2), 197–204 (2004)

    Article  Google Scholar 

  • Bahill, A.T., Baldwin, D.G.: Describing baseball pitch movement with right-hand rules. Comput. Biol. Med. 37, 1001–1008 (2007)

    Article  Google Scholar 

  • Bahill, A.T., Baldwin, D.G.: Mechanics of baseball pitching and batting, Chapter 16. In: Ghista, D. (ed.) Applied Biomedical Engineering Mechanics, pp. 445–488. CRC Press and Taylor & Francis, Boca Raton (2008)

    Google Scholar 

  • Bahill, A.T., Karnavas, W.J.: Determining ideal baseball bat weights using muscle force-velocity relationships. Biol. Cybern. 62, 89–97 (1989)

    Article  Google Scholar 

  • Bahill, A.T., Karnavas, W.J.: The ideal baseball bat. New Sci. 130(1763), 26–31 (1991)

    Google Scholar 

  • Baldwin, D.G., Bahill, A.T.: A model of the bat’s vertical sweetness gradient. In: Hubbard, M., Mehta, R.D., Pallis, J.M. (eds.) The Engineering of Sport 5, vol. 2, pp. 305–311. Proceedings of the 5th International Engineering of Sport Conference, September 13–16, 2004, Davis, CA, International Sports Engineering Association (ISEA), Sheffield (2004)

    Google Scholar 

  • Box, J.F.: Gosset, fisher, and the t distribution. Am. Stat. 35(2), 61–66 (1981)

    MathSciNet  Google Scholar 

  • Brach, R.M.: Mechanical Impact Dynamics: Rigid Body Collisions. John Wiley & Sons, New York, 1991, republished in (2007)

    Google Scholar 

  • Crisco, J. J., Greenwald, R. M., Blume, J. D. and Penna, L. H., Batting performance of wood and metal baseball bats, Medicine & Science in Sports & Exercise, 1675–1684, 2002.

    Google Scholar 

  • Cross, R.: Mechanics of swinging a bat. Am. J Physics. 77(1), 36–43 (2009)

    Article  Google Scholar 

  • Cross, R.: Physics of Baseball and Softball. Springer New York (2011)

    Google Scholar 

  • Dadouriam, H.M.: Analytic Mechanics for Students of Physics and Engineering, p. 248. D. Van Nostrand Co., New York (1913)

    Google Scholar 

  • Drane, P.J., Sherwood, J.A., Jones, J.W., Connelly, T.P.: The effect of baseball construction on the game of baseball (P275). In: The Engineering of Sport 7, pp. 681–688. Springer, Paris (2008)

    Chapter  Google Scholar 

  • Duris, J., Smith, L.: Evaluation test methods used to characterize softballs. In: Hubbard, M., Mehta, R.D., Pallis, J.M. (eds.) Proceedings of the 5th Conference of Engineering of Sport. International Sports Engineering Association (ISEA), vol. 2, pp. 80–86. ISBN 0-9547861-1-4 (2004)

    Google Scholar 

  • Fallon, L.P., Sherwood, J.A.: Performance Comparison of the 1999 and 2000 Major League Baseballs. University of Massachusetts Lowell. (2000). http://baseball.physics.illinois.edu/UML2000.pdf

  • Ferreira da Silva, M.F.: Meaning and usefulness of the coefficient of restitution. Eur. J. Phys. 28, 1219–1232 (2007). https://doi.org/10.1088/0143-0807/28/6/019

    Article  Google Scholar 

  • Fleisig, G.S., Zheng, N., Stodden, D.F., Andrews, J.R.: Relationship between bat mass properties and bat velocity. Biomechanics Symposia 2001. University of San Francisco California. (2001)

    Google Scholar 

  • Fleisig, G.S., Zheng, N., Stodden, D.F., Andrews, J.R.: Relationship between bat mass properties and bat velocity. Sports Eng. 5, 1–8 (2002)

    Google Scholar 

  • Higuchi, T., Nagami, T., Nakata, H., Watanabe, M., Isaka, T., Kanosue, K.: Contribution of visual information about ball trajectory to baseball hitting accuracy. PLoS One. 11, e0148498 (2016). https://doi.org/10.1371/journal.pone.0148498

    Article  Google Scholar 

  • King, K., Hough, J., McGinnis, R.: A new technology for resolving the dynamics of a swinging bat. Sports Eng. 15, 41–52 (2012)

    Article  Google Scholar 

  • Kensrud, J.R., Nathan, A.M., Smith, L.V.: Oblique collisions of baseballs and softballs with a bat. Am. J. Physiol. 85, 503–509 (2017)

    Article  Google Scholar 

  • Koenig, K., Mitchell, N.D., Hannigan, T.E., Cluter, J.K.: The influence of moment of inertia on baseball/softball bat swing speed. Sports Eng. 7, 105–117 (2004)

    Article  Google Scholar 

  • Milanovich, M., Nesbit, S.M.: A three-dimensional kinematic and kinetic study of the college-level female softball swing. J Sports Sci Med. 13(1), 180–191 (2014.) PMCID: PMC3918556

    Google Scholar 

  • Nathan, A. M. Dynamics of the baseball-bat collision, American Journal of Physics, 68(11), 979–990 (2000)

    Google Scholar 

  • Nathan, A.M.: Characterizing the performance of baseball bats. Am. J. Physiol. 71, 134–143 (2003)

    Article  Google Scholar 

  • Nathan, A.M., Smith, L.V., Faber, W.L., Russell, D.A.: Corked bats, juiced balls, and humidors: the physics of cheating in baseball. Am. J. Physiol. 79(6), 575–580 (2011)

    Article  Google Scholar 

  • Nathan, A.M., Cantakos, J., Kesman, R., Mathew, B., Lukash, W.: Spin of a batted baseball, 9th conference of the international sports engineering association (ISEA). Procedia Eng. 34, 182–187 (2012). https://doi.org/10.1016/j.proeng.2012.04.032

    Article  Google Scholar 

  • Sears, F.W., Zemansky, M.W., Young, H.D.: University Physics. Addison-Wesley, Reading MA (1976)

    Google Scholar 

  • Watts, R.G., Bahill, A.T.: Keep Your Eye on the Ball: The Science and Folklore of Baseball. W. H. Freeman and Co., New York (1990)

    Google Scholar 

  • Watts, R.G., Bahill, A.T.: Keep Your Eye on the Ball: Curve Balls, Knuckleballs, and Fallacies of Baseball. W. H. Freeman and Co., New York (2000)

    Google Scholar 

  • Welch, C.M., Banks, S.A., Cook, F.F., Draovitch, P.: Hitting a baseball: a biomechanical description. J. Orthopaed Sports Phys Ther. 22, 193–201 (1995)

    Article  Google Scholar 

  • Willman, D.: BaseballSavant. https://baseballsavant.mlb.com/statcast_search (2017). Accessed Sept 2017

  • Williams, T., Underwood, J.: The Science of Hitting. Simon and Schuster, New York (1982)

    Google Scholar 

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Bahill, A.T. (2018). Equations for Bat-Ball Collisions. In: The Science of Baseball. Springer, Cham. https://doi.org/10.1007/978-3-319-67032-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-67032-4_3

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