ME
ME 6201 Introduction to Continuum Mechanics
D.L. McDowell
Stress
Module 41: Balance of Angular Momentum
Outline of This Module:
Balance of Angular Momentum
Symmetry of Cauchy Stress Tensor
ME
ME 6201 Introduction to Continuum Mechanics
D.L. McDowell
8/19/2015
Lecture 2: State-Space Modeling & Linearization
State-Space Modeling of Physical Systems
Mechanical, fluid, electrical, and mixed examples
Transfer Function Representation
Linearization
Overview
In the last lecture, we provided an
introduction t
9/2/2015
Lecture 4: Time Response of Linear Systems
Free and Forced Responses of
Linear Systems
Time Response of LTI Systems
Laplace Transform Method
Simulation Examples
Overview
Time response of a system
provides time history of its states given
initial
8/28/2015
Lecture 3: Canonical Forms
Change of State Variables
Controllable Canonical Form
Observable Canonical Form
Jordan Canonical Form
Overview
Last Lecture: State space modeling and
linearization. In this lecture well look at
Nonuniqueness of state-
9/21/2015
Module 8: Modal Decomposition I
Decoupling State Transformation
Eigenvalue Problem
Distinct and Repeated Eigenvalues
Matlab Examples
Motivation
Modal Decomposition can be used for
Decoupling of LTI Systems
Stability and Modal analysis
Model R
9/23/2015
Lecture 11: Stability
Definition of Stability
Stability of LTI systems
BIBO Stability
Relationship between Stability Types
MATLAB Example
Motivation
Stability is the minimum requirement of any
control system
Main goal of a feedback control syste
9/8/2015
Lecture 5: Discrete-Time Systems
Introduction
Discrete-Time Equivalent of
Continuous-Time Systems
Time Response Analysis
Matlab Examples
Overview
Last Lecture: Time Response Analysis of
Continuous-Time Systems.
This lecture:
Difference State Eq
Lecture 13: Observability
Definition of Observability
Observability Criterion for Linear
Sytems
Observability Rank Test for LTI
Systems
Physical & MATLAB Examples
Motivation
Observability is the ability to estimate
the states from output measurement
Obser
Lecture 12: Controllability
Definition of Controllability
Controllability Criterion for Linear
Sytems
Controllability Rank Test for LTI
Systems
Physical & MATLAB Examples
Motivation
Controllability analysis is important for
feedback control system design
8/16/2015
State-Space Model
Mathematical Modeling
Basic Definitions
State Equations
Illustrative Example
System Definition in MATLAB
Mathematical Modeling (MM)
Mathematical model of a dynamic system is a
set of mathematical equations (e.g., differential
e