Game Development Reference
In-Depth Information
We won't repeat Dr. Jorgensen's development of the model here; instead, we'll show you
how to solve the resulting equations:
Those equations can be found in the Technical Appendix—Section 4 of Dr. Jorgensen's
book—but are listed here for convenience.
Equation 1:
Equation 2:
Table 19-3 explains what each symbol represents.
Table 19-3. Symbols used in golf swing model
Symbol
Meaning
J
Mass moment of inertia of the rod representing the arm. Units are kg-m 2 .
I
Mass moment of inertia of the rod representing the club. Units are kg-m 2 .
M c
Mass of the club. Units are kg.
R
Length of the rod representing the arm. Units are m.
S
First moment of the rod representing the club about the wrist axis (where the club rod connects to the arm rod). Units
are kg-m.
α
Angle swept by arm rod from initial backswing position. Units are radians.
β
g
Acceleration due to gravity. Constant 9.8 m/s 2 .
Θ
Angle between arm rod and vertical axis. Units are radians.
a
Horizontal acceleration of the shoulder. Units are m/s 2 .
S A
First moment of the arm rod about the shoulder axis. Units are kg-m.
Q α
Torque applied at the shoulder to the arm rod. Units are N-m.
Q β
Torque applied at the wrist joint to the club rod. Units are N-m.
These equations represent a coupled system of nonlinear differential equations. They
are coupled in that they both depend on the unknown quantities α and β. They are
clearly differential equations, as they both include time derivatives of the unknown