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Jack H

12.4.1 Euler-Lagrange

• This method uses a Lagrangian energy operator to calculate torques

L

( θ

i

, ω ) = K

i

– P

i

 

L( θ ,ω ) = ∑ Ki – ∑ Pi

i

 

 

 

 

i

 

 

 

 

 

 

 

 

d

 

∂

 

 

 

 

∂

 

 

 

 

 

 

 

----

 

 

 

 

 

L

 

–

 

L

 

=

Q

 

dt

∂ ω

i

 

i

 

∂ θ i

 

 

i

 

 

 

i

where,

L = lagrangian

K = kinetic energy of link ‘i’ P = potential energy of link ‘i’ Q = forces and torques

• For a typical link,