Beckham and Bats
Stokes Theorem: Line Integrals, Vorticity, and You
Free kick!
Velocity field of spinning ball
https://www.comsol.com/blogs/magnus-effect-world-cup-match-ball/
Under pressure: Magnus effect
http://biomechanicsofthesetshot.blogspot.com/2014/06/the-question.html
http://scienceblogs.com/dotphysics/2010/09/07/the-curving-soccer-ball/
Magnus Effect:
Force depends on rotation
Depeux et al, 2010. http://iopscience.iop.org/article/10.1088/1367-2630/12/9/093004/pdf
Theory/Model/Real life
Stokes Theorem Example
Image credit: Maria Belk, Bard College
Vortex Shedding
Kelvin’s Theorem: Vorticity Conserved (action = reaction)
Stokes’ Theorem true around ANY closed curve
Going batty!
Going batty
Wake Vorticity Structure
Wake Structure: Vortices