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CS545—Contents X
Lagrange’s Method of Deriving Equations of Motion for
Rigid Body Systems
Lagrange’s Equation
Generalized Coordinates
Potential Energy
Kinetic Energy
Properties of the Dynamics Equations
Reading Assignment for Next Class
See http://wwwclmc.usc.edu/~cs545
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View Full Document Lagrange’s Equations
The Lagrangian (a potential function) is
Lagrange’s Equations are:
Generalized Coordinates
Any set of coordinates that complete describes a dynamical system
Lagrangian is coordinate free
Generalized Forces
The corresponding forces or torques applied along the generalized
coordinates
Includes friction, external, and motor forces (non conservative forces)
L
=
T

U
d
dt
∂
L
∂
˙
θ
i
−
∂
L
∂θ
i
=
τ
i
Kinetic Energy
Potential Energy
Lagrangian
Equation of Motion
m
l
Motor
Gravity g
I
˙
˙
θ
+
mgl
sin
(
) =
τ
T
=
1
2
I
˙
2
U
=
mgl
1
−
cos
(
)
L
=
T

U
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This note was uploaded on 11/06/2010 for the course CS 101 at Cornell University (Engineering School).
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