Newtonian physics and motion of a wiggling rope

[Fascheue]

What types of objects does Newtonian mechanics deal with? Is it just rigid bodies? I’m not sure how Newton’s laws could explain something like the motion of a wiggling rope.

 

[anorlunda]

It may not seem obvious, but Newtonian mechanics to apply to a rope.

To make is easier to visualize, imagine it as a wiggling chain. Each link is a rigid body and you can use Newton's laws in their familiar form. Make the link size arbitrarily small and you have a continuous rope. The physical laws don't change with link size.

 

[Fascheue]

It may not seem obvious, but Newtonian mechanics to apply to a rope.

To make is easier to visualize, imagine it as a wiggling chain. Each link is a rigid body and you can use Newton's laws in their familiar form. Make the link size arbitrarily small and you have a continuous rope. The physical laws don't change with link size.

Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?

 

[jbriggs444]

Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?

Finite Element Analysis is probably too clunky to use on such a problem -- possible, but inefficient. One could make simplifying assumptions so that the differential equations are tractable. That's still Newtonian physics.

There are wave equations for strings and ropes that are based on Newtonian physics plus the simplifying assumption of uniform tension.