<s>
Dynamic	B-Application
simulation	I-Application
(	O
or	O
dynamic	O
system	O
simulation	O
)	O
is	O
the	O
use	O
of	O
a	O
computer	B-Application
program	I-Application
to	O
model	O
the	O
time-varying	O
behavior	O
of	O
a	O
dynamical	O
system	O
.	O
</s>
<s>
The	O
equation	O
is	O
solved	O
through	O
numerical	B-Algorithm
integration	I-Algorithm
methods	O
to	O
produce	O
the	O
transient	O
behavior	O
of	O
the	O
state	O
variables	O
.	O
</s>
<s>
A	O
numerical	B-Application
simulation	I-Application
is	O
done	O
by	O
stepping	O
through	O
a	O
time	O
interval	O
and	O
calculating	O
the	O
integral	O
of	O
the	O
derivatives	O
through	O
numerical	B-Algorithm
integration	I-Algorithm
.	O
</s>
<s>
This	O
is	O
why	O
most	O
old	O
simulation	O
programs	B-Application
are	O
simply	O
differential	O
equation	O
solvers	O
and	O
delegate	O
solving	O
difference-equations	O
to	O
“	O
procedural	O
program	O
segments.	O
”	O
Some	O
dynamic	O
systems	O
are	O
modeled	O
with	O
differential	O
equations	O
that	O
can	O
only	O
be	O
presented	O
in	O
an	O
implicit	O
form	O
.	O
</s>
<s>
The	O
first	O
applications	O
of	O
computer	B-Application
simulations	I-Application
for	O
dynamic	O
systems	O
was	O
in	O
the	O
aerospace	O
industry	O
.	O
</s>
<s>
Commercial	O
uses	O
of	O
dynamic	B-Application
simulation	I-Application
are	O
many	O
and	O
range	O
from	O
nuclear	O
power	O
,	O
steam	O
turbines	O
,	O
6	O
degrees	O
of	O
freedom	O
vehicle	O
modeling	O
,	O
electric	O
motors	O
,	O
econometric	O
models	O
,	O
biological	O
systems	O
,	O
robot	O
arms	O
,	O
mass-spring-damper	O
systems	O
,	O
hydraulic	O
systems	O
,	O
and	O
drug	O
dose	O
migration	O
through	O
the	O
human	O
body	O
to	O
name	O
a	O
few	O
.	O
</s>
<s>
Simulation	O
is	O
also	O
used	O
in	O
computer	O
games	O
and	O
animation	O
and	O
can	O
be	O
accelerated	O
by	O
using	O
a	O
physics	O
engine	O
,	O
the	O
technology	O
used	O
in	O
many	O
powerful	O
computer	O
graphics	O
software	B-Application
programs	I-Application
,	O
like	O
3ds	B-Language
Max	I-Language
,	O
Maya	B-Language
,	O
Lightwave	B-Device
,	O
and	O
many	O
others	O
to	O
simulate	O
physical	O
characteristics	O
.	O
</s>
