Re: [Phys-L] Conical Pendulum Diff Equations

[brian whatcott <betwys1@sbcglobal.net>]

This appears to be the case of a night - several days really - when the 
hound did not bark. Not a squeak from the folks who are at least as 
strong in math as in physical mechanics. Wonder why?

Maybe a conical pendulum is not a pendulum that we know and love: one 
that exchanges energy between kinetic and potential. Perhaps although 
it's a mass swinging on a light suspension, it has more of the wheel 
turning on a vertical axis: it is spun up and losses will spin it down, 
if it is not regularly, or continuously aided with an increment of 
angular velocity?
One easily relates string deflection angle, angular velocity and mass. 
Tan theta = v^2 / r.g  r the  horizontal radius of rotation, v 
tangential velocity, angular momentum conserved;  the ballerina spins up 
at some point if her arms are drawn in....

But where does the rate of any of these quantities affect another? 
Having voiced that puzzlement, it is easy to find papers to explain that 
matters can get tricky quite fast when examining the conical pendulum. 
Is there a central turning pivot for a torsionally stiff string? is 
there an axial oscillation tending to stabilize an inverted conical  
pendulum? That sort of thing!   :-)

Brian W



On 9/6/2018 10:05 AM, Roberto Carabajal via Phys-l wrote:
> Hello
>
> have trouble finding the detailed deduction of the differential equations
> for the Conical Pendulum with dumping. I would appreciatte any comments it
> or where to search.
> My best regards,
>
> Roberto
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