Degenerating force in Lagrangian mechanics

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SUMMARY

The discussion focuses on deriving the equations of motion for three coupled pendula, specifically incorporating a resistive degenerative force affecting the central pendulum due to submersion in a liquid. The user has successfully calculated the normal modes using the Lagrangian approach without resistance. However, integrating a damping term into the equations of motion for the middle pendulum presents challenges, particularly in maintaining the integrity of modal analysis. The inclusion of viscous damping complicates the modal analysis, potentially requiring advanced techniques such as complex modes.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with coupled oscillators
  • Knowledge of viscous damping and its effects on motion
  • Experience with modal analysis techniques
NEXT STEPS
  • Research the application of viscous damping in Lagrangian systems
  • Study the derivation of equations of motion for damped oscillators
  • Explore complex modes in modal analysis
  • Investigate numerical methods for simulating damped coupled pendula
USEFUL FOR

Physicists, mechanical engineers, and students studying dynamics and oscillatory systems, particularly those interested in the effects of damping on coupled pendula.

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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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