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

Wrist-cock angle. Units are radians.

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