Skip to Main Content
Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
Density Function f
Y
(y) =
1
3
1
(1)
2π
exp
(y + 4)
2
18(1)
2
, −∞ 0
91
4.10. Given the fluid drag equation F
D
= C
D
V
2
, where C
D
is a constant (with dimensions) and
f
V
(v) = 0.1, for the range 10 v 20, derive f
F
D
and sketch both density functions.
Solution: For this case there are two roots
v = ±
F
D
/C
D
, and
dv
dF
D
= ±
1
2
F
D
C
D
.
The general transformation is given by
f
F
D
(F
D
) =
1
2
C
D
F
D
1
f
V
3
F
D
C
D
+ f
V
3
F
D
C
D
2
u (F
D
) ,
where u(·) is the unit step function. However, since v has a positive range we must drop the negative root.
Therefore,
f
F
D
(F
D
) =
1
2
C
D
F
D
1
10
u (F
D
)
=
1
20 ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Adaptive Learning Methods for Nonlinear System Modeling

Adaptive Learning Methods for Nonlinear System Modeling

Danilo Comminiello, Jose C. Principe
Mathematical Methods in Dynamical Systems

Mathematical Methods in Dynamical Systems

S. Chakraverty, Subrat Kumar Jena

Publisher Resources

ISBN: 9781439849897