Neville de Mestre. The mathematics of projectiles in sport

Queensland, Australia: Bond University. 1990. – 186 p.A large number of sporting events contain the motion of a projectile; yet research papers have appeared only intermittently on the mathematical techniques associated with projectiles in sport. A recent book by Hart and Croft (1988) presents a subset of these techniques for a small selection of events. The aim of the current book is to present a unified collection of the many problems that can be tackled and of all the mathematical techniques that can be employed.Motion under gravity alone
Gravity
Velocity and Position Vectors
Point of Impact
The Vertex of the Trajectory
Projection from a Different Level
Inclined Plane
Enveloping Parabola
Dimensionless Equations
Exercises
Motion in a linear resisting medium
Velocity and Position Vectors
Maximum Height
Impact Time to the Horizontal Plane
Range on the Horizontal Plane
Envelopes
Inclined Planes
Curve of Safety
Exercises
Motion in a non-linear resisting medium
Non-linear Drag
Cartesian Equations for Power-law Drag
Acceleration Components
Power-law Solution
Applications of the Power-law Solution
Other Non-linear Drag Functions
Exercises
The basic equations and their numerical solution
The Basic Equations
Ballistic Table Computations
Simple Application
Range Tables
Variations within the Basic Equations
Graphical Technique
Exercises
Small drag or small gravity
Perturbation Techniques
Gravity or Drag Perturbations
Exercises
Corrections due to other effects
Effects Other Than Constant Gravity and Variable Drag
Coriolis Corrections
Gravity Corrections
Density, Temperature, Pressure and Humidity Variations
Lift and Sideways Aerodynamic Corrections
Wind Corrections
Overturning Moment
Differential Corrections
Exercises
Spin effects
Overcoming Yaw
Spin Stabilisation of Shells
Spinning Spheres
Fluid Dynamics
The Magnus Effect
The Swing of a Cricket Ball
Spinning Seeds
The Equations of Motion for a Spinning Shell Exercises
Projectiles in sport and recreation
Classes of Projectiles
Drag-to-weight Ratio
Shot-put and Hammer Throw
Basketball
Tennis, Table Tennis and Squash
Badminton
Golf
Cricket
Baseball
Soccer
Rugby and Australian Rules Football
Javelin
Discus, Frisbee and Flying Ring
Long Jump, High Jump and Ski Jump
Boomerangs
Water Jets
Cars and Cycles
Seed Dispersal
The Longest Throw or Kick
Exercises