Game Physics Engine Development, 2nd Edition

14.6 Exercises 385

14.6 Exercises

Exercise 14.1

An object has an inertia tensor of

⎡

⎢

⎣

a 00

0 b 0

00c

⎤

⎥

⎦

What is its inverse inertia tensor? If you kno w how to invert a matrix algebraically,

you can do that to solve this problem. Alternatively, you can either work through the

matrix inversion code by hand, or experiment with its results until you see the pattern

(it shouldn’t be difficult to spot).

Exercise 14.2

If we have a basis matrix for con tact coordinates C, and a basis matrix for an object’s

local coordinates M, write an expression for transforming a vector in the object’s loc al

coordinates into c ontact coordinates.

Exercise 14.3

If we have a basis matrix for con tact coordinates C, and a basis matrix for an object’s

local coordinates M , write