The Mathematics of Projectiles in Sport Book

	Preface	ix
1.	Motion Under Gravity Alone
1.1	Gravity	1
1.2	Velocity and Position Vectors	2
1.3	Point of Impact	4
1.4	The Vertex of the Trajectory	5
1.5	Projection from a Different Level	9
1.6	Inclined Plane	11
1.7	Enveloping Parabola	14
1.8	Dimensionless Equations	21
1.9	Exercises	22
2.	Motion in a Linear Resisting Medium
2.1	Velocity and Position Vectors	24
2.2	Maximum Height	28
2.3	Impact Time to the Horizontal Plane	28
2.4	Range on the Horizontal Plane	30
2.5	Envelopes	31
2.6	Inclined Planes	32
2.7	Curve of Safety	35
2.8	Exercises	37
3.	Motion in a Non-Linear Resisting Medium
3.1	Non-linear Drag	39
3.2	Cartesiau Equations for Power-law Drag	39
3.3	Acceleration Components	41
3.4	Power-law Solution	43
3.5	Applications of the Power-law Solution	49
3.6	Other Non-linear Drag Functions	52
3.7	Exercises	55
4.	The Basic Equations and Their Numerical Solution
4.1	The Basic Equations	58
4.2	Ballistic Table Computations	60
4.3	Simple Application	63
4.4	Range Tables	65
4.5	Variations within the Basic Equations	66
4.6	Graphical Technique	68
4.7	Exercises	74
5.	Small Drag or Small Gravity
5.1	Perturbation Techniques	77
5.2	Gravity or Drag Perturbations	81
5.3	Exercises	89
6.	Corrections Due to Other Effects
6.1	Effects Other Than Constant Gravity and Variable Drag	92
6.2	Coriolis Corrections	93
6.3	Gravity Corrections	97
6.4	Density, Temperature, Pressure and Humidity Variations	103
6.5	Lift and Sideways Aerodynamic Corrections	105
6.6	Wind Corrections	108
6.7	Overturning Moment	114
6.8	Differential Corrections	115
6.9	Exercises	117
7.	Spin Effects
7.1	Overcoming Yaw	119
7.2	Spin Stabilisation of Shells	120
7.3	Spinning Spheres	122
7.4	Fluid Dynamics	123
7.5	The Magnus Effect	126
7.6	The Swing of a Cricket Ball	129
7.7	Spinning Seeds	131
7.8	The Equations of Motion for a Spinning Shell	131
7.9	Exercises	134
8.	Projectiles in Sport and Recreation
8.1	Classes of Projectiles	135
8.2	Drag-to-weight Ratio	136
8.3	Shot-put and Hammer Throw	139
8.4	Basketball	141
8.5	Tennis, Table Tennis and Squash	143
8.6	Badminton	144
8.7	Golf	145
8.8	Cricket	148
8.9	Baseball	150
8.10	Soccer	152
8.11	Rugby and Australian Rules Football	153
8.12	Javelin	155
8.13	Discus, Frisbee and Flying Ring	156
8.14	Long Jump, High Jump and Ski Jump	158
8.15	Boomerangs	161
8.16	Water Jets	162
8.17	Cars and Cycles	165
8.18	Seed Dispersal	165
8.19	The Longest Throw or Kick	166
8.20	Exercises	167
	References	168
	Index	173