including external forces with KanesMethod of LagrangesMethod

[Kevin Bockstael]

Hi

I would like to include a periodic external force into a multiple mass damper-system. My first thought was to include it in the forcelist (using KanesMethod)

which would then become something like in the code below. (where b is the frequency of the periodic force)

This however, returns an error whenever i want to integrate the dynamical equations.

Does anyone know how to include the external force f(t) = sin(b*t), so i can integrate the dynamical equations? 

Thanks

q1,u1,q2,u2 = dynamicsymbols('q1 u1 q2 u2')

q1d, q2d = dynamicsymbols('q1 q2',1)

m1,c1,k1, m2,c2,k2, g,t,b = symbols('m1 c1 k1 m2 c2 k2 g t b')

N = ReferenceFrame('N')

O=Point('O')

O.set_vel(N,0)

P = Point('P')

P.set_vel(N,-u1*N.y)

Q=Point('Q')

Q.set_vel(N,-(u2+u1)*N.y)

kd=[q1d-u1,q2d-u2]

FL = [(P,(2*k1*q1-k1*q2+c1*u1)*N.y),(Q,((k1+k2)*q2-k1*q1+c2*u2+sin(b*t))*N.y)]

[Jason Moore]

Kevin,

You are correct, you should include the force, sin(b*t), in the force list. Then KanesMethod, for example will give you:

Mx' = f(x, t)

The force, sin(b*t), will be explicitly in the f(x, t) portion. You can then think of it as:

Mx' = f_(x) + u(t)

where u(t) = sin(b * t)

Then when you want to integrate the equations you must make sure that t is available for the ode right hand side.

def rhs(x, t, ...)

return solve(M, f_(x) + u(t))

Something like that. If you show a more complete piece of code that I can run, then I can give you more specific advice.

Jason
moorepants.info
+01 530-601-9791

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[Jason Moore]

Kevin,

Here is another example of doing that:

https://github.com/pydy/pydy#usage-1

Jason
moorepants.info
+01 530-601-9791

[Kevin Bockstael]

Jason,

The problem was indeed that 't' was not available as a variable for odeint. 

Thanks a lot!

Op dinsdag 22 april 2014 21:38:06 UTC+2 schreef Jason Moore:

[Jason Moore]

Great! If you get a nice example problem working, we'd love to have it added to the examples directory in the pydy repository. It will help others with issues like this.

Jason
moorepants.info
+01 530-601-9791

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/8a04fd07-a909-4a00-8995-a1c07ff06eec%40googlegroups.com.