1. Beckham and Bats Stokes Theorem: Line Integrals, Vorticity, and You

2. Free kick!

3. Velocity field of spinning ball https://www.comsol.com/blogs/magnus-effect-world-cup-match-ball/

4. Under pressure: Magnus effect http://biomechanicsofthesetshot.blogspot.com/2014/06/the-question.html http://scienceblogs.com/dotphysics/2010/09/07/the-curving-soccer-ball/

5. Magnus Effect: Force depends on rotation Depeux et al, 2010. http://iopscience.iop.org/article/10.1088/1367-2630/12/9/093004/pdf

6. Theory/Model/Real life

7. Stokes Theorem Example Image credit: Maria Belk, Bard College

8. Vortex Shedding Kelvin’s Theorem: Vorticity Conserved (action = reaction) Stokes’ Theorem true around ANY closed curve

9. Going batty!

10. Going batty Wake Vorticity Structure

11. Wake Structure: Vortices