Game Development Reference

In-Depth Information

Chapter 13 Summary

Force Equation

()

The acceleration

a
of an object multiplied by its mass
m
is equal to the sum of

the forces acting on it:

N

F

()

()

x
.

()

t

=

mt

a

=

mt

i

i

=

1

Second-Order Differential Equations

The general solution to the homogeneous second-order differential equation

′′

()

′

()

()

x

t

+

xt

+

xt

=

0

is given by

()

rt

r t

x t

=

e

+

e

,

1

2

where

a

1

2

r

=−

+

a

−

4

b

1

22

1

a

2

r

=−

−

a

−

4

b

.

2

22

If
1

rr r

==

, then the general solution is given by

2

()

rt

rt

x t

=

e

+

te

.

If
r
and
r
are complex numbers, then the general solution can also be written as

()

αt

(

)

xt

=

e

C βtC βt

cos

+

sin

,

1

2

where

a

α

=−

2

1

2

β

=

4

ba

−

.

2

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