Dynamics of thin string

[jpittelo]

Does anybody know how to compute the dynamics of a thin string, whose extremity (border condition) is given a certain displacement, withtout taking into account elasticity phenomena (infinitely thin) ? (Such as variational dynamical principles ?)

 

Thanx.

[arkain101]

N^x/ (Freq * (-1) *C) = (M*V^2)

 

:) ever just wrote out nonsense equations before?

[jpittelo]

You mean nonsense like

 

v=sqrt(E/rho)....?? I wonder how scientists can earn their life with formulas.....?? ANd you ?

[arkain101]

Joking mood.

[Erasmus00]

Does anybody know how to compute the dynamics of a thin string, whose extremity (border condition) is given a certain displacement, withtout taking into account elasticity phenomena (infinitely thin) ? (Such as variational dynamical principles ?)

 

If you are neglecting elasticity phenomena, I assume you wish to neglect waves? As such, the shape of the string will be determined entirely by considering the need to minimize the gravitational potential energy of the string. This is an old problem, the solutions that minimize the potential of your hanging rope are the hyperbolic trig functions sinh and cosh, so the general solution is a linear combination of the two. If you move the two end points of the string, you simply adjust the solution so that you have a combination of sinh and cosh that match the new boundary conditions.

-Will

[jpittelo]

Yes...my question, more precisely, was : can we compute the statical solutions (Euler-Lagrange) for two infinitesimally different configurations (variational claculation that does not require elasticity, aso), and then find the dynamics between both equilibria ?

[Qfwfq]

I still can't quite understand what you have been asking about... what I don't get at the moment is the meaning of:

find the dynamics between both equilibria

In what sense the "dynamics between them"?

:)