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The Mathematics of Projectiles in Sport : Australian Mathematical Society Lecture Series - Neville de Mestre

The Mathematics of Projectiles in Sport

Australian Mathematical Society Lecture Series

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

Paperback Published: 18th June 1990
ISBN: 9780521398572
Number Of Pages: 188

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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.

"...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

Prefacep. ix
Motion Under Gravity Alone
Gravityp. 1
Velocity and Position Vectorsp. 2
Point of Impactp. 4
The Vertex of the Trajectoryp. 5
Projection from a Different Levelp. 9
Inclined Planep. 11
Enveloping Parabolap. 14
Dimensionless Equationsp. 21
Exercisesp. 22
Motion in a Linear Resisting Medium
Velocity and Position Vectorsp. 24
Maximum Heightp. 28
Impact Time to the Horizontal Planep. 28
Range on the Horizontal Planep. 30
Envelopesp. 31
Inclined Planesp. 32
Curve of Safetyp. 35
Exercisesp. 37
Motion in a Non-Linear Resisting Medium
Non-linear Dragp. 39
Cartesiau Equations for Power-law Dragp. 39
Acceleration Componentsp. 41
Power-law Solutionp. 43
Applications of the Power-law Solutionp. 49
Other Non-linear Drag Functionsp. 52
Exercisesp. 55
The Basic Equations and Their Numerical Solution
The Basic Equationsp. 58
Ballistic Table Computationsp. 60
Simple Applicationp. 63
Range Tablesp. 65
Variations within the Basic Equationsp. 66
Graphical Techniquep. 68
Exercisesp. 74
Small Drag or Small Gravity
Perturbation Techniquesp. 77
Gravity or Drag Perturbationsp. 81
Exercisesp. 89
Corrections Due to Other Effects
Effects Other Than Constant Gravity and Variable Dragp. 92
Coriolis Correctionsp. 93
Gravity Correctionsp. 97
Density, Temperature, Pressure and Humidity Variationsp. 103
Lift and Sideways Aerodynamic Correctionsp. 105
Wind Correctionsp. 108
Overturning Momentp. 114
Differential Correctionsp. 115
Exercisesp. 117
Spin Effects
Overcoming Yawp. 119
Spin Stabilisation of Shellsp. 120
Spinning Spheresp. 122
Fluid Dynamicsp. 123
The Magnus Effectp. 126
The Swing of a Cricket Ballp. 129
Spinning Seedsp. 131
The Equations of Motion for a Spinning Shellp. 131
Exercisesp. 134
Projectiles in Sport and Recreation
Classes of Projectilesp. 135
Drag-to-weight Ratiop. 136
Shot-put and Hammer Throwp. 139
Basketballp. 141
Tennis, Table Tennis and Squashp. 143
Badmintonp. 144
Golfp. 145
Cricketp. 148
Baseballp. 150
Soccerp. 152
Rugby and Australian Rules Footballp. 153
Javelinp. 155
Discus, Frisbee and Flying Ringp. 156
Long Jump, High Jump and Ski Jumpp. 158
Boomerangsp. 161
Water Jetsp. 162
Cars and Cyclesp. 165
Seed Dispersalp. 165
The Longest Throw or Kickp. 166
Exercisesp. 167
Referencesp. 168
Indexp. 173
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521398572
ISBN-10: 0521398576
Series: Australian Mathematical Society Lecture Series
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 188
Published: 18th June 1990
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.94 x 15.32  x 1.25
Weight (kg): 0.27

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