Degenerating force in Lagrangian mechanics

[laird HT]

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!

 

[Dr.D]

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.

 

[astrokreng]

Degenerating force in Lagrangian mechanics refers to a resistive force that acts against the motion of a system, causing it to dissipate energy and eventually come to a stop. In your case, it seems that the central pendulum is experiencing this type of force due to its submersion in a liquid.

To incorporate this degenerating force into your system, you will need to modify the Lagrangian equations of motion to include the resistive force term. This can be done by adding a term in the Lagrangian function that represents the energy dissipated by the resistive force. This term will depend on the velocity of the pendulum, as well as the properties of the liquid such as its viscosity.

You can then use the modified Lagrangian equations to derive the equations of motion for your system, taking into account the degenerating force. This will allow you to study the behavior of the system with the resistive force included.

I would recommend consulting with a mentor or colleague who has experience with Lagrangian mechanics to help you with this derivation. Additionally, there are many resources available online that can provide guidance and examples for incorporating degenerating forces into Lagrangian mechanics.

Overall, incorporating the degenerating force into your system will provide a more realistic and accurate representation of the behavior of the pendulum system. I wish you the best of luck in your research.