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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