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Chapter 2 - Laplace Trnasform
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Complex Numbers, Laplace Transformations
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Lecture 1: 04 10112023Mechanical
system () Equations (Math realm
System dynamics is a
unified approach to
analyze dynamic systems, be they mechanical,
electrical, fluid, thermal, etc...
We use an abstraction or mathematical representation of the
system.
Real
simplifyingtons Approximate physicallaws
- Mathematical
system
> representation model
-output
(car motion)
eg: car
driving I DOF
&x
d own a
road i M
sinusoidal
nc
S
bumpy road
Wheel
follows
=>
x
y Y
(Wtlizirpur road)
theroad. = sin
C
any
Physicallaws: Newton 2nd law more complex (multiple Dof)
(I anumption
mathematical model:
e
mx + c(x 0
y) + x(x y) I
- -
me
=
↳ Iti
↳ Caplan representation
Transfer function.
This can be used
for wide
approach variety of
a
the
systems. The
goal:
show
unified representations
& available
analytical tool to
analyze conno
them.
, Definition:
dynamic system: the
A output of the
system depends, not only on the
Output-input: differential present values of the input but also on
past values
equeat
A static system: the output depends only on the input
"N
output input: algebraic
-
&
output
*
input F
if masslers: static, instantaneous
acc.
~ if massifinertia => takes a
while
t move
H
dynamic
↳
"N
Linear
systems: in the
governing differential equations, the dependant
variables and their derivatives linear combination
appear only as
x 5x+10x -line
eg; + = 0
5x"
e.g. x + +10 = 0
-now heat
x 5x + 5xx 0 linear
eg: + =
-> non
We can use superposition to analyze linear systems.
Model simplicity is
accuracy
"
"The ideal model is one that is simple and accurate
-often, we must
compromise between
simplicity and
accuracy
- Choiceis made based on resources (time, money, people.)
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