The dynamics of a soccer free kick

1
The dynamics of a soccer free kick
http//www.youtube.com/watch?vneLMQymZnz0
http//www.youtube.com/watch?vc5bRoWtGcWU
http//www.youtube.com/watch?vceFtwgSe3PM
2
Analysis of Beckham free kick Ireson, 2001
Distance of 20 - 25 m.
Foot velocity of 20 m/s
Ball leaves the foot 25 m/s
Force perp. path 3-4 N
Drag force 3 N
Mass (FIFA) 0.45 kg.
Spin 60 rad/s
3
A
B (3.66,54.5)
(-3.66,54.5)
(34.3, 54.5)
D (9.15, 38.04)
(-9.15, 38.04) C
P
O
(34.3, 0.0)
4
FL
v
Vector ? coming out of the plane
5
Reference point on the body
Vector u coming out of the plane
Center of rotation fixed to the body
6
v
?
z
t
?t
?n
y
x
7
Equations of Motion

• Particle in 3-D subject to thrust, gravity and
  drag
• X - State vector is 6x1

• 6 State Equations

8
v
k
?
FL
t
j
i
FG
FD