Damping an n-body pendulum
in [Physics]
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From: Olumide on 3 Aug 2010 20:20 Hi - I would like to simulate human hair as an n-body pendulum system. However, the equations of the system are such that the system is undamped and thus oscillate forever. For example, (2-body pendulum): http://en.wikipedia.org/wiki/Double_pendulum I would like to to incorporate the energy loss due to drag. What form would this energy loss take? Thanks, - Olumide
From: Androcles on 3 Aug 2010 21:20 "Olumide" <50295(a)web.de> wrote in message news:287ea407-324e-4080-8ad5-372e2fb9ea9e(a)i24g2000yqa.googlegroups.com... | Hi - | | I would like to simulate human hair as an n-body pendulum system. | However, the equations of the system are such that the system is | undamped and thus oscillate forever. For example, (2-body pendulum): | http://en.wikipedia.org/wiki/Double_pendulum | | I would like to to incorporate the energy loss due to drag. What form | would this energy loss take? | | Thanks, | | - Olumide | Simple enough. Reduce the angular velocity the pendulum arms swing through and radiate the energy difference as sound and/or heat from friction in the joints (bearings). If your joint is a bending of the hair it still warms up with flexing, the same way car tyres warm up as you flex them. Listen to a car passing by (carefully) and ignore the sound of the engine. The tyres hiss, quite loudly, radiating sound.
From: eratosthenes on 4 Aug 2010 06:43 On Aug 3, 9:20 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > | I would like to to incorporate the energy loss due to drag. What form > | would this energy loss take? That is not terribly difficult to derive, although generalizing to n- bodies and obtaining a useful solution may be another matter. T get the Lagrangian for the system you need the following, where % is the angle with the vertical: x = L * cos(%) y = - L * sin(%) dx/dt = L * sin(%) * d%/dt dy/dt = L * cos(%) * d&/dt The damping can be modeled as a generalized force, call it friction, viscosity or whatever you like and give A the appropriate units: F_x = - A * L * cos(%) * d&/dt F_x = - A * L * sin(%) * d&/dt From there the basic one dimensional derivation is cake, the rest is up to you. Patrick
From: Androcles on 4 Aug 2010 07:56
"eratosthenes" <rehamkcirtap(a)gmail.com> wrote in message news:15586daf-3d70-4460-853b-be7879299294(a)z30g2000prg.googlegroups.com... | I would like to to incorporate the energy loss due to drag. What form | would this energy loss take? Why would you want to do that, snipping daehtihs(a)gmail.com? |