This review describes and classifies the trajectories of sports projectiles that have spherical
symmetry, cylindrical symmetry, or (almost) no symmetry. This classification allows us to …

The term knuckleball in sporting jargon is used to describe a ball that has been launched
with minimal spin, resulting in a trajectory that is erratic and unpredictable. This …

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a
thin compressible elastic wall, a situation that arises in a variety of technological and natural …

Using plain white and chequered footballs, we evaluated observers' sensitivity to rotation
direction and the effects of ball texture on interceptive behaviour. Experiment 1 …

Two vortices of opposite sign in two dimensions merely move along parallel lines. We show
that even a small buoyancy completely changes this dynamics. When the vortices are of …

The trajectory of a soccer ball, kicked with a spin to curve it into the goal, is strongly
influenced by aerodynamic factors such as the Magnus force. Several studies using a wind …

Magnus gliders are spinning toys displaying spectacular looped trajectories when launched
at large velocity. These trajectories originate from the large amplitude of the Magnus force …

Untitled Page 1 Page 2 Articles Mathematics of Soccer Alda Carvalho, Carlos Pereira dos
Santos, Jorge Nuno Silva ISEL & Cemapre-ISEG, ISEC & Cima, FCUL acarvalho@adm.isel.pt …

It is the fifth minute of the 2018 FIFA World Cup semi-final England-Croatia. Kieran Trippier
has just scored England's first free kick goal at a World Cup for 12 years. Prior to the free …

This research aims to develop various models of design skills training techniques, develop
initial product, test a small group, large group test, and implement test the effectiveness of …