EN 137: Advanced Engineering Mechanics
Professor K.-S. Kim
Date: Jan. 26, 2012
Lecture 1
Principle Virtual Work (PVW)
(1) Admissible kinematics
(2) Virtual work 0, equilibrium
Example:
D
h3
h2
L
L
h1 sin , h1' sin
2
2
L
h1 h1' h1 cos
2
<Note> sin sin
EN 137: Advanced Engineering Mechanics
Professor K.-S. Kim
Date: Jan. 31, 2012
Lecture 2
Contents of Dynamics:
Particle Dynamics
Work and Energy Methods
Rigid Body Dynamics
Vibration and Time Response
Running
mv 2
h 1 v gh : Flying is part of running,
mg
EN 137: Advanced Engineering Mechanics
Professor K.-S. Kim
Date: Feb. 02, 2012
Lecture 3
Kinematics of Motion (Position, Velocity, Acceleration and Constraints)
Motivation: Principle of Virtual Work (Lagranges equations)
(1) Position of a Material Point (
EN 137: Advanced Engineering Mechanics
Professor K.-S. Kim
Date: Feb. 7, 2012
Lecture 4
Dynamics of a Collective System of Masses
Moving Coordinates
x p xo ' x
v p x p xo ' x v o ' x
a p p v o '
x
x
For a vector A t
o'
dA(t ) A(t )
A
dt
t rel
A A rel v
EN 137: Advanced Engineering Mechanics
Professor K.-S. Kim
Date: Feb. 9, 2012
Lecture 5
Rigid Body Motion in a Vector Representation
Momentum: Linear momentum p , angular momentum H
Recall
v p v 0 v rel r
r
a p a 0 a rel r r 2 v rel
rp
Define linear momen
EN 137: Advanced Engineering Mechanics
Lecture 8
1
Professor K.-S. Kim
Date: Feb. 23, 2012
2
3
Goal:
Solve the histories of two generalized coordinates ( x, ) in the system.
Kinetic energy:
(1)
x(1) x x(1) x
x(2) x sin x(2) x cos
y(2) cos y(2) sin
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