Lagrangian Mechanics: The Half Atwood Machine

Here is the solution for the equation of motion for a half Atwood machine using Lagrangian mechanics

[@Cloudserious]

It really helps me a lot.thx!!!❤

[@DotPhysics]

Happy to help!

[@mastershooter64]

Will you please cover lagrangian field theory? maybe using EM and GR as examples, like the electromagnetic lagrangian and the einstein-hilbert action??

[@ericknutson8310]

My mechanics professor assigned us the same problem, but the pulley is raised up a bit and we haven’t touched Lagrangians yet. Trying to get a formula for mass 1,s (x..)

[@DotPhysics]

If the pulley is being accelerated up, you can still do this with Newton's second law. Just draw a force diagram for both masses, it should work.

[@souparnochakraborty1928]

Hey! the x1' was -y2' but you didn't consider the negative while substituting it in the T1 equation. It must be m1-m2 , otherwise => y1'' = -g doesn't make sense here as m2 is free falling

[@siriuss_]

Arigato PE! :3

[@amirb715]

how do you add the friction into the Lagrangian?

[@DotPhysics]

If you want to add static friction - it's pretty simple. It's just a force of constraint (think of a ball rolling without slipping down a ramp). However, if you want to have kinetic friction then it's very tough. The problem is that friction is not conservative so you can't turn it into a potential. If you have a problem with kinetic friction, it might be better to use something other than Lagrangian.

[@abedhamid159]

halo...why lagrange put this function L=T-U

[@fizixx]

🥳

[@vkktr-dt3iq]

what pen is that?

[@DotPhysics]

it's a paper mate flair size medium