Rotational Systems
MECH432: Dynamic System Analysis
03
1
Todays Goals
You should be able to
Model simple Mechanical Rotational Systems
2
Rotational Systems
3
Variables
: angular displacement in
radians (rad)
Angular displacements are measured
with res
Quiz 2: 10 minutes
Given the FBD equations, represent the dynamics in terms of an
appropriate set of state variables, find and input-output equation
governing the output x1(t), and represent the input-output using a block
diagram
M1 !
x1 + B ( x!1 z!2 ) +
Quiz 1: 10 minutes
Given that x3(t) is the input to the system and x1 is the output
1. Draw the free body diagram(s)
2. Compute the FBD modeling equation(s) in terms of x1, x2, and x3(t)
MECH 432 - SHAMMAS
Free body diagram
M1
x1
B ( x1 z2 )
K1 ( x1 x3 (
This picture was taken in Damnernsaduak, Thailand. This relates to the lesson as it
is an ecosystem, also shown a population.
And give good tidings to those who believe and do righteous deeds that
they will have gardens [in Paradise] beneath which rivers
NEWTONS LAWS OF MOTION
The motion of a particle is governed by Newtons three laws of
motion.
First Law: A particle originally at rest, or moving in a straight
line at constant velocity, will remain in this state if the resultant
force acting on the partic
WORK AND ENERGY
Another equation for working kinetics problems involving
particles can be derived by integrating the equation of motion
(F = ma) with respect to displacement.
By substituting at = v (dv/ds) into Ft = mat, the result is
integrated to yield
CONSERVATIVE FORCE
A force F is said to be conservative if the work done is
independent of the path followed by the force acting on a particle
as it moves from A to B. In other words, the work done by the
force F in a closed path (i.e., from A to B and th
PROCEDURE FOR ANALYSIS
Free Body Diagram
Establish your coordinate system and draw the particles
free body diagram showing only external forces. These
external forces usually include the weight, normal forces,
friction forces, and applied forces. Show th
NORMAL & TANGENTIAL COORDINATES
When a particle moves along a
curved path, it may be more
convenient to write the equation of
motion in terms of normal and
tangential coordinates.
The normal direction (n) always points toward the paths
center of curvature
POWER
Power is defined as the amount of work performed per unit
of time.
If a machine or engine performs a certain amount of work,
dU, within a given time interval, dt, the power generated can
be calculated as
P = dU/dt
Since the work
can be expressed as
Principle of
Physical Modeling
MECH431: Dynamic System Analysis
Lecture 1
Sunday, September 15, 13
1
Todays Goals
You should be able to
use a systematic methodology for modeling
complex systems
model simple mechanical, electrical and
hydraulic systems
Electrical Systems
MECH432: Dynamic System Analysis
04
Todays Goals
You should be able to
Model Electrical Systems
Across and Through
Variables
Mechanical System
Electrical System
Fluid System
Power
P = Fv
P = v12i
P = p12Q
Energy Dissipation
Mechanical
1st and 2nd Order
Systems
MECH432: Dynamic System Analysis
06
1
Various forms of solutions
So far we have been exposed to two methods
of formulating a problem:
State variable solutions
Input output differential equations
We proposed solving these meth
Principle of
Physical Modeling
MECH431: Dynamic System Analysis
Lecture 2
System Models
Sunday, September 15, 13
1
Todays Goals
You should be able to
Write a model in various forms
Sunday, September 15, 13
As State variables
As Input-output
As a Block Di
Electrical Systems
MECH432: Dynamic System Analysis
04
1
Todays Goals
You should be able to
Model Electrical Systems
2
Electrical Circuits Example
3
Coupling by
Potentiometer
4
Resistive coupling
A variable resistance can be controlled by
mechanical mot