Skip to Main Content
Flight Dynamics Principles, 2nd Edition
book

Flight Dynamics Principles, 2nd Edition

by Michael V. Cook
February 2011
Beginner to intermediate content levelBeginner to intermediate
488 pages
17h 21m
English
Butterworth-Heinemann
Content preview from Flight Dynamics Principles, 2nd Edition
Ch05-H6927.tex 20/6/2007 16: 34 Page 124
124 Flight Dynamics Principles
Since the input is constant the convolution integral is easily evaluated and
z(t) = e
t
z(0) +
1
[e
t
I]V
1
Bu
k
(5.97)
Thus the transform, equation (5.82), enables the state vector to be determined:
x(t) = Ve
t
[V
1
x(0) +
1
V
1
Bu
k
] A
1
Bu
k
e
At
[x(0) +A
1
Bu
k
] A
1
Bu
k
(5.98)
The derivation of equation (5.98) makes use of the following property of the matrix
exponential:
1
e
t
e
t
1
(5.99)
and the similarity transform:
A
1
= V
1
V
1
(5.100)
Again, the output response is obtained by substituting the state vector x(t), equation
(5.98), into the output equation to give
y(t) = CVe
t
[V
1
x(0)
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

Commercial Airplane Design Principles

Commercial Airplane Design Principles

Pasquale M. Sforza
Theory and Practice of Aircraft Performance

Theory and Practice of Aircraft Performance

Ajoy Kumar Kundu, Mark A. Price, David Riordan

Publisher Resources

ISBN: 9780750669276