Homework 4
2 0
0
0
1 . Find eAt using three dierent methods.
1. Given A = 1
0 2 2
2. For the matrix given in problem 1, nd sin(A).
3. For the matrix given in the problem 1, nd the modal decomposition of
the response of x = Ax when x(0) = [111]T .
4. Find
ME451: Control Theory
2/15/2005
Linearization
Reference: Sections 2.102.11, Control Systems Engineering, N.S. Nise
The analytical models for most mechanical engineering systems are nonlinear. A linear system
has output(s) linearly dependent on its input
EE 422G Notes: Chapter 7
Instructor: Cheung
Use State Variable to represent circuits
Lets start with a simple example:
L=1H
R=2
+
u(t)
a
y(t)
C=1F
i
+


NOTE: in this chapter, we will use u(t) (not to be confused with the step function)
to denote the in
HW #2
Due: 10/16/2012 at 3:05 pm
1
1. Find a state equation to describe the network shown in the gure below. Find also its
transfer function.
2. Consider the mechanical system below. Let I denote the moment of inertia of the bar
and block about the hinge.
CLOSED CHAIN SYSTEMS
EML 5215
BACKGROUND
The most frequent type of system in engineering dynamics is an open chain system, where one
end of the system is attached to a base body by some kind of joint while the one end of the
system is completely unconstra
CLOSED CHAIN SYSTEMS
EML 5215
BACKGROUND
The most frequent type of system in engineering dynamics is an open chain system, where one
end of the system is attached to a base body by some kind of joint while the one end of the
system is completely unconstra
HOMEWORKASSIGNMENTS
EML5215
As noted in the syllabus, nearly all of the problems in the homework assignments have the
answers given in the book. It is therefore up to you to work the problem until you get the
correctanswer.Ifyouhaveahardtimewithaparticula
Solution for Homework 5
ME243A/ECE230A
Fall 2007
Exercise 1
The computation of the reachable subspace in continuous time can be handled
easily introducing the concepts of inner product, orthogonal complement of a
subspace and adjoint operator.
Given a vec
EML 5215
Exam 2
Fall 2015
89 December 2015
1
What Allowed During Examination
You may use any books, your personal notes, or electronic aid, provided that you find the material
on your own without having it provided to you by anyone else (either implicitl
EML 5215
Exam 1
Fall 2015
1617 October 2015
1
What Allowed During Examination
You may use any books, your personal notes, or electronic aid, provided that you find the material
on your own without having it provided to you by anyone else (either implicit
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Dynamics of a Gyroscope
Anil V. Rao
2
Example 11
A symmetric top is modeled as a rigid body B that moves while in contact with an
inertially fixed point O. Assuming that gravity acts vertically downward, determine
three differential equations that describ
EML 5215
Exam 2
Spring 2015
2122 April 2015
1
What Allowed During Examination
You may use any books, your personal notes, or electronic aid, provided that you find the material
on your own without having it provided to you by anyone else (either implicit
EML 5215
Exam 1
Spring 2015
25 February 2015
1
What Allowed During Examination
You may use any books, your personal notes, or electronic aid, provided that you find the material
on your own without having it provided to you by anyone else (either implicit
EML 5215 ANALYTICAL DYNAMICS
FALL 2015
Syllabus (a.k.a. our contract for the semester)
COURSE INSTRUCTOR: Dr. Riccardo Bevilacqua, MAEA 308, [email protected], 3523926230. Office hours: Mondays and Wednesdays, 4:10pm5:40pm, starting August
31st, 2015, end
TEXTBOOKANDSOFTWARELOGISTICS
EML5215
TherequiredtextbookforEML5215isEngineeringMechanicsOnlineParts1and2byThomasR.
Kane and David A. Levinson. The textbook must be purchased with a credit card through the
followingwebsite:
http:/www.motiongenesis.com/MGWe