[SciPy-user] Bicycle Wheel Precession
David Goldsmith
David.L.Goldsmith@noaa....
Fri Apr 27 13:33:51 CDT 2007
As a generalization of David's comment below, I would emphasize that you
check that the numerical values you're using in your simulation (e.g.,
for things like proportionality constants, initial conditions, etc.)
accurately reflect those inherent in your experimental apparatus, both
wrt value and units. For instance, whether or not what you're observing
is nutation or precession, if your numerical values are such that the
amplitude of the sinusoid is small, it would appear to be "near" a
constant function...
Another David
David Huard wrote:
> The wheel's rotation looks too slow, and the effect you're seeing
> would then be nutation, which I think is normal given your initial
> conditions.
>
> David
>
> Reference: Goldstein's Classical Mechanics, p 217-219.
>
>
> 2007/4/26, Ryan Krauss <ryanlists@gmail.com
> <mailto:ryanlists@gmail.com>>:
>
> I am trying to teach my dynamics students about teh precession of a
> bicycle wheel like in this video:
>
> http://commons.bcit.ca/physics/video/precession.shtml
> <http://commons.bcit.ca/physics/video/precession.shtml>
>
> If the x axis is along the axle of the wheel and the z axis points up,
> I think the motion can be modeled using the following ode:
>
> def NewtonEuler(x,t,M,I):
> Ixx=I[0]
> Iyy=I[1]
> Izz=I[2]
> wx=x[0]
> wy=x[1]
> wz=x[2]
> dxdt=zeros(3,)
> dxdt[0]=((Iyy-Izz)*wy*wz+M[0])/Ixx
> dxdt[1]=((Izz-Ixx)*wx*wz+M[1])/Iyy
> dxdt[2]=((Ixx-Iyy)*wx*wy+M[2])/Izz
> return dxdt
>
> I use this function along with integrate.odeint in the attached file,
> but the surprising thing is that wz is sinusoidal rather than nearly
> constant. Experimentally, I see nearly constant precession.
>
> Can anyone help me find what is wrong with my approach?
>
> Thanks,
>
> Ryan
>
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