TM BOOKLET Berlin Wcup 2017 V1.0
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On the Mechanics of the Bow and Arrow 1
On the Mechanics of the Bow and Arrow 1 B.W. Kooi Groningen, The Netherlands 1983 1B.W. Kooi, On the Mechanics of the Bow and Arrow PhD-thesis, Mathematisch Instituut, Rijksuniversiteit Groningen, The Netherlands (1983), Supported by ”Netherlands organization for the advancement of pure research” (Z.W.O.), project (63-57) 2 Contents 1 Introduction 5 1.1 Prefaceandsummary.............................. 5 1.2 Definitionsandclassifications . .. 7 1.3 Constructionofbowsandarrows . .. 11 1.4 Mathematicalmodelling . 14 1.5 Formermathematicalmodels . 17 1.6 Ourmathematicalmodel. 20 1.7 Unitsofmeasurement.............................. 22 1.8 Varietyinarchery................................ 23 1.9 Qualitycoefficients ............................... 25 1.10 Comparison of different mathematical models . ...... 26 1.11 Comparison of the mechanical performance . ....... 28 2 Static deformation of the bow 33 2.1 Summary .................................... 33 2.2 Introduction................................... 33 2.3 Formulationoftheproblem . 34 2.4 Numerical solution of the equation of equilibrium . ......... 37 2.5 Somenumericalresults . 40 2.6 A model of a bow with 100% shooting efficiency . .. 50 2.7 Acknowledgement................................ 52 3 Mechanics of the bow and arrow 55 3.1 Summary .................................... 55 3.2 Introduction................................... 55 3.3 Equationsofmotion .............................. 57 3.4 Finitedifferenceequations . .. 62 3.5 Somenumericalresults . 68 3.6 On the behaviour of the normal force -