Degenerating force in Lagrangian mechanics

AI Thread Summary
The discussion focuses on deriving equations of motion for three coupled pendula, specifically incorporating a resistive degenerative force on the central pendulum due to liquid submersion. The user has successfully calculated normal modes without resistance using the Lagrangian approach and seeks guidance on integrating the damping effect. It is noted that while adding a damping term to the equations of motion is possible, it won't alter the modal analysis significantly. Incorporating viscous damping complicates the modal analysis, as it may require complex modes, which can be challenging. Overall, the integration of resistance into the system requires careful consideration of its effects on the dynamics.
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HELP!

I am currently working on the derivation of the equations of motion for three coupled pendula, The mass and length of each pendulum is the same, but the central pendulum has some sort of resistive degenerative force due to submersion in a liquid. I have calculated the normal modes without the resistance of the system using the lagrangian approach.

How can i do this, with the resistance integrated into the system?
Any help would be greatly appreciated!
 
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If you have the three equations of motion without the damping force, simply re--write them to include a damping term acting on the middle pendulum.

This is not going to change your modal analysis of the system, however, assuming that you include viscous damping. There is no simple way to include viscous damping in a modal analysis (it can be done using complex modes, but that is a can of worms!), so you are right back where you started as far as the modal analysis is concerned.
 

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