The Mathematics of Projectiles in Sport

By: Neville de Mestre, Chris Heyde (Contribution by), J. H. Loxton (Contribution by), W. D. Neumann (Contribution by), Charles Pearce (Contribution by)

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Paperback | 18 June 1990

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188 Pages

Dimensions(cm)
22.86 x 15.24 x 1.09

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The mathematical theory underlying many sporting activities is of considerable interest to both applied mathematicians and sporting enthusiasts alike. Here Professor de Mestre presents a rigorous account of the techniques applied to the motion of projectiles. This equips the reader for the final section of the book in which an enlightening collection of sporting applications is considered, ranging from the high jump to frisbees and soccer to table tennis. The presentation should be accessible to most undergraduate science students and provides an ideal setting for the development of mathematical modeling techniques.

Industry Reviews

"...delightful book which treats a special set of dynamical systems of considerable interest." Victor G. Szebehely, American Mathematical Monthly "The writing is clear and the book is very free of errors. The early chapters could well serve advanced undergraduates as a source of interesting problems; the later chapters and references could provide research material for graduate students or faculty." Mathematical Reviews "...an interesting book that presents some difficult material in a terse but readable style." Richard C. Roberts, Journal of College Science Teaching

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Preface	p. ix
Motion Under Gravity Alone
Gravity	p. 1
Velocity and Position Vectors	p. 2
Point of Impact	p. 4
The Vertex of the Trajectory	p. 5
Projection from a Different Level	p. 9
Inclined Plane	p. 11
Enveloping Parabola	p. 14
Dimensionless Equations	p. 21
Exercises	p. 22
Motion in a Linear Resisting Medium
Velocity and Position Vectors	p. 24
Maximum Height	p. 28
Impact Time to the Horizontal Plane	p. 28
Range on the Horizontal Plane	p. 30
Envelopes	p. 31
Inclined Planes	p. 32
Curve of Safety	p. 35
Exercises	p. 37
Motion in a Non-Linear Resisting Medium
Non-linear Drag	p. 39
Cartesiau Equations for Power-law Drag	p. 39
Acceleration Components	p. 41
Power-law Solution	p. 43
Applications of the Power-law Solution	p. 49
Other Non-linear Drag Functions	p. 52
Exercises	p. 55
The Basic Equations and Their Numerical Solution
The Basic Equations	p. 58
Ballistic Table Computations	p. 60
Simple Application	p. 63
Range Tables	p. 65
Variations within the Basic Equations	p. 66
Graphical Technique	p. 68
Exercises	p. 74
Small Drag or Small Gravity
Perturbation Techniques	p. 77
Gravity or Drag Perturbations	p. 81
Exercises	p. 89
Corrections Due to Other Effects
Effects Other Than Constant Gravity and Variable Drag	p. 92
Coriolis Corrections	p. 93
Gravity Corrections	p. 97
Density, Temperature, Pressure and Humidity Variations	p. 103
Lift and Sideways Aerodynamic Corrections	p. 105
Wind Corrections	p. 108
Overturning Moment	p. 114
Differential Corrections	p. 115
Exercises	p. 117
Spin Effects
Overcoming Yaw	p. 119
Spin Stabilisation of Shells	p. 120
Spinning Spheres	p. 122
Fluid Dynamics	p. 123
The Magnus Effect	p. 126
The Swing of a Cricket Ball	p. 129
Spinning Seeds	p. 131
The Equations of Motion for a Spinning Shell	p. 131
Exercises	p. 134
Projectiles in Sport and Recreation
Classes of Projectiles	p. 135
Drag-to-weight Ratio	p. 136
Shot-put and Hammer Throw	p. 139
Basketball	p. 141
Tennis, Table Tennis and Squash	p. 143
Badminton	p. 144
Golf	p. 145
Cricket	p. 148
Baseball	p. 150
Soccer	p. 152
Rugby and Australian Rules Football	p. 153
Javelin	p. 155
Discus, Frisbee and Flying Ring	p. 156
Long Jump, High Jump and Ski Jump	p. 158
Boomerangs	p. 161
Water Jets	p. 162
Cars and Cycles	p. 165
Seed Dispersal	p. 165
The Longest Throw or Kick	p. 166
Exercises	p. 167
References	p. 168
Index	p. 173
Table of Contents provided by Syndetics. All Rights Reserved.

The Mathematics of Projectiles in Sport

At a Glance

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