[SciPy-user] Bicycle Wheel Precession

[David Huard]

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 at 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
>
> 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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