Lagrangian Mechanics: Chain Sliding Off a Table

[@rmandra]

Thanks!

[@DotPhysics]

thank you for your support!

[@leonardofacchin1452]

Your enthusiasm is contagious! Thanks for this video, even though I knew that I should have never watched it, because now I'm obsessed with trying to solve the same problem with an elastic chain... 😀

[@DotPhysics]

glad you enjoyed it. I really have fun with physics.

[@ajejebrazor4936]

Lovely stuff going on here! Hope for the springy challenge!

[@fizixx]

Great problem and the mix of math and python is always a winner! 🐍

[@dogspaghetti7118]

11:02 Shouldn’t it be Bb²•e^(-bt)?

[@mrslave41]

1:24 λ=linear density of chain =entire mass / entire length =M/R

[@mrslave41]

1:41 x=length of chain on the table y (s) = length of chain hanging off table

[@ruhailmir]

Amazing stuff as always, Thanks. We can also use something called "Verlet Integration" as an alternative to connecting the masses with springs. It's a very efficient and powerful method.

[@mrslave41]

0:56 R = entire length of chain M = entire mass of chain

[@mrslave41]

2:00 R=x+y(s)

[@mrslave41]

2:34 R=s+(-x) x=s-R x=-(R-s)

[@martyrosadil9989]

Love your videos ❤❤❤ Can you make small videos about solving some question ⁉️

[@mrslave41]

2:40 you already lost me 😢😢😢😢😢. please slow down when explaining. 😢😢😢

[@padraiggluck2980]

Let’s do a slinky.

[@godphysics2473]

There is no mention to the initial condition to start the motion of the chain; is a simple case, ideal physical situation?

[@abicol6010]

Assuming no friction, as long as part of the chain is hanging off, the chain will fall. It would be a lot harder to figure out with friction. Although I would like to see him solve that.

[@pashaw8380]

@@abicol6010 Not that hard, just use the Rayleigh dissipation function and combine it with the Euler Lagrange equation to form the system's dynamic equation: (d/dt)(∂ℒ/∂ṡ)-(∂ℒ/∂s)+(∂R/∂ṡ)=0 in which R(ṡ)=[1/(0+1)]·∑ᵢ₌₁[(C₁)(ṡ₁)⁰⁺¹]=Cṡ and C=F(µ). Later do a little ODE then you'll get the answer identical to the one obtained from the Newtonian method. If you want the complete process I can show it here.