Answers to the Exercises - 3D Math Primer for Graphics and Game Development - page 791

Body front:
r ′ = (0, 1.00, 2.25) − (0, 1.01, 1.05) = (0, −0.01, 1.20)

2
4 241

3
5

2
4 (−0.01) 2 + 1.20 2

3
5

0 0 −0 (−0.01) −0 1.20

J ′ =

0 2 + 1.20 2

(kg m 2 )

0 521 0 + 1000

−0 (−0.01) −(−0.01) 1.20

0 0 387

0 2 + (−0.01) 2 −0 1.20 −(−0.01) 1.20

2
4 1680

3
5

0 0

(kg m 2 ) = 0 1960 12.0

0 12.0 387

Body middle:
r ′ = (0, 125, 75) − (0, 1.01, 1.05) = (0, 0.24, −0.30)

2
4 197

3
5

2
4 0.24 2 + (−0.30) 2

3
5

0 0 −0 0.24 −0 (−0.30)

J ′ = 0 2 + (−0.30) 2 (kg m 2 ) 0 313 0 + 600 −0 0.24 −0.24 (−0.30)

0 0 285

0 2 + 0.24 2

−0 (−0.30) −0.24 (−0.30)

2
4 286

3
5

0 0

(10 2 kg m 2 )

0 367 43.2

=

0 43.2 320

Body rear:
r ′ = (0, 1.00, −1.20) − (0, 1.01, 1.05) = (0, −0.01, −2.25)

2
4 213

3
5

2
4 (−0.01) 2 + (−2.25) 2

3
5

0 0 −0 (−0.01) −0 (−2.25)

J ′ = (kg m 2 ) 0 2 + (−2.25) 2 0 325 0 + 400 −0 (−0.01) −(−0.01) (−2.25)

0 0 155

0 2 + 0.01 2

−0 (−2.25) −(−0.01) (−2.25)

2
4 22.4

3
5

0 0

(10 2 kg m 2 )

= 0 23.5 −0.09

0 −0.09 1.55

Front left wheel:
r ′ = (−1.00, 0.35, 2.30) − (0, 1.01, 1.05) = (−1.00, −0.66, 1.25)

2
4 3.06

3
5

0 0

J ′ = (kg m 2 )

0 1.70 0

0 0 1.70

2
4 (−0.66) 2 + 1.25 2

3
5

−(−1.00) (−0.66) −(−1.00) 1.25

(kg m 2 )

(−1.00) 2 + 1.25 2

+ 50 −(−1.00) (−0.66) −(−0.66) 1.25

(−1.00) 2 + (−0.66) 2 −(−1.00) 1.25 −(−0.66) 1.25

2
4 103

3
5

−33.0 62.5

(kg m 2 ) = −33.0 130 41.3

62.5 41.3 73.5

Front right wheel:
r ′ = (1.00, 0.35, 2.30) − (0, 1.01, 1.05) = (1.00, −0.66, 1.25)

2
4 3.06

3
5

0 0

J ′ = (kg m 2 )

0 1.70 0

0 0 1.70

2
4 (−0.66) 2 + 1.25 2

3
5

−(1.00) (−0.66) −(1.00) 1.25

(kg m 2 ) (1.00) 2 + 1.25 2

+ 50 −(1.00) (−0.66) −(−0.66) 1.25

(1.00) 2 + (−0.66) 2 −(1.00) 1.25 −(−0.66) 1.25

2
4 103

3
5

33.0 −62.5

(kg m 2 )

= 33.0 130 41.3

−62.5 41.3 73.5