Dynamics of coin tossing – influence of air resistance

• Autorzy: Grabski, J. , Strzałko, J. , Kapitaniak, T.
• Konferencja: Symposium Vibrations In Physical Systems (23 ; 28-31.05.2008 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

In following paper some aspects of tossed coin dynamics are presented. Firstly: one-, two-, and three-dimensional coin models are presented. More general case of nonsymmetric or nonhomogenous coin is described. It is assumed that the coin is released above a plain floor. Free fall of the coin as well as the coin motion including air resistance forces and moments are analysed. Some results of numerical solution simulations are shown.

Słowa kluczowe

PL

rzut monetą; dynamika; opór powietrza; symulacja numeryczna

EN

coin tossing; coin dynamics; air resistance; numerical simulation

• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2008
• Tom: Vol. 23
• Strony: 145--150
• Opis fizyczny: Bibliogr. 8 poz., il. (w tym kolor.), wykr.

Twórcy

autor

Grabski, J.

• Technical University of Łódź, Machines Dynamics Division, Poland, 90-924 Łódź, ul. Stefanowskiego 1/15,

autor

Strzałko, J.

• Technical University of Łódź, Machines Dynamics Division, Poland, 90-924 Łódź, ul. Stefanowskiego 1/15

autor

Kapitaniak, T.

• Technical University of Łódź, Machines Dynamics Division, Poland, 90-924 Łódź, ul. Stefanowskiego 1/15

Bibliografia

• [1] J.B. Keller, The probability of heads, American Mathematical Monthly, 93, 3 (1986) 191 – 197.
• [2] P. Diaconis, S. Holmes, R. Montgomery, Dynamical Bias in the Coin Toss. Society for Industrial and Applied Mathematics, 49, 2 (2007) 211 – 235.
• [3] V.Ž. Vulović, R.E. Prange, Randomness of true coin toss. Physical Review A, 33/1 (1986) 576 – 582.
• [4] T. Mizuguchi, M. Suwashita, Dynamics of Coin Tossing. Progress of Theoretical Physics Supplement, 161 (2006) 274 – 277.
• [5] J. Grabski, J. Strzałko, P. Perlikowski, T. Kapitaniak, Wykorzystanie kwaternionów do opisu dynamiki ciała. Analiza ruchu rzucanej monety. Materiały Kongresu Mechaniki Polskiej (2007).
• [6] P.E. Nikrevesh, Computer-Aided Analysis of Mechanical Systems. Prentice- Hall International, Inc., Englewood Cliffs 1988.
• [7] J. Diebel, Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors. http://ai.stanford.edu/~diebel/ (May, 2007).
• [8] Mathematica 4. Standard Add-on Packages. Wolfram Media, 1999.