Game Development Reference

In-Depth Information

⎡

⎣

⎤

⎦

2

5
mr
2

00

5
mr
2
0

00
5
mr
2

2

I

=

0

where
m
is the mass and
r
is the radius of the sphere.

The same sphere that is just a shell (i.e., has all its mass around the surface of the

sphere) has the following inertia tensor:

⎡

⎣

⎤

⎦

2

3
mr
2

00

3
mr
2
0

00
3
mr
2

2

I

=

0

A.3.3

C
YLINDER

A cylinder, of uniform density, whose principal axis is along the Z axis, has an inertia

tensor of

⎡

⎤

12
mh
2

1

1

4
mr
2

+

0

0

⎣

⎦

1

1

I

=

12
mh
2

4
mr
2

0

+

0

1

2
mr
2

0

0

where
m
is the mass,
r
is the radius of the cylinder, and
h
is its height.

A.3.4

C
ONE

A cone, of uniform density, whose principal axis is along the Z axis, has an inertia

tensor of

⎡

⎣

⎤

⎦

3

3

80
mh
2

20
mr
2

+

0

0

80
mh
2

3

20
mr
2

3

I

=

0

+

0

3

10
mr
2

0

0

where
m
is the mass,
r
is the radius of the cone, and
h
is its height. Unlike the other

shapes, the cone's center of mass isn't through its geometric center. Assuming the

center of the base of the cone is at the origin, the center of mass is at

⎡

⎣

⎤

⎦

0

0

1

4
h

where
h
is the height of the cone, as before.