Thanks for the follow up, sorry for my bad understanding of the method,
I'm not a mechanics guy...
Here is the notebook without defining any dependent coordinates. This
yields the same equations, so it's fine.
http://nbviewer.ipython.org/github/glyg/Notebooks/blob/master/kt_sim/minimum%20Linear%20Force%20Velocity.ipynb?flush_cache=true
The only thing that is puzzling me is that the linearization doesn't
correspond the equations of motion (because as F=1-u, it can't be
written in the form M*[dq, du] = A*[q, u], the constant term is dropped.
I - wrongly - thought that defining dependent speeds would get around that.
Thnaks for the help any way, I'll cook something up from here.
Best,
Guillaume
Le 13/01/2015 19:43, Jason Moore a écrit :
I think you are using a velocity constraint when it is not needed. You
have your generalized coordinates: q1 and q2. L is simply sqrt(q1**2 +
q2**2), right? I think you need to define ell = sqrt(q1**2 + q2**2).
The velocity constraint functionality of KanesMethod is primarily in
place to deal with non-holonomic constraints, which you don't have. It
can probably be manipulated to be used for other things, but I don't
think it is useful for this problem.
Jason
moorepants.info <http://moorepants.info>
+01 530-601-9791
On Tue, Jan 13, 2015 at 2:48 AM, Guillaume Gay <[email protected]
<mailto:[email protected]>> wrote:
A follow up:
I believe this comment in kanes.py (l. 206) is related. In my
case, the constant is not negligeable.
# Form of non-holonomic constraints is B*u + C = 0.
# We partition B into independent and dependent columns:
# Ars is then -B_dep.inv() * B_ind, and it relates dependent
speeds
# to independent speeds as: udep = Ars*uind, neglecting the C
term.
B_ind = self._k_nh[:, :p]
B_dep = self._k_nh[:, p:o]
self._Ars = -B_dep.LUsolve(B_ind)
Best,
Guillaume
Le 13/01/2015 09:45, Guillaume Gay a écrit :
Hi Jason, thanks a lot for the help.
I simplified a lot the definitions, and used directly the
velocities in the definitions.
So the KanesMethod class can be instanciated, and the
`to_linearizer` method works. The only issue I'm left with is
that the M, A, B matrices output by the `linearizer.linearize()`
are not consistent with the equations of motion - when you
compare the f_3 equation with the uquations from M[dot q, dot u]
= A[q, u]: the constant term is droped - compare cells In [8] and
In [10] & In [11] on the notebook bellow:
http://nbviewer.ipython.org/github/glyg/Notebooks/blob/master/kt_sim/minimum%20Linear%20Force%20Velocity.ipynb
I'm not sure if this is my fault, or just that the linearizer
wont work in my case because of the form of the contraint...
Best,
Guillaume
Le 12/01/2015 19:10, Jason Moore a écrit :
I meant: p1.set_vel(N, u1 * N.x)
Jason
moorepants.info <http://moorepants.info>
+01 530-601-9791 <tel:530-601-9791>
On Mon, Jan 12, 2015 at 10:08 AM, Jason Moore
<[email protected] <mailto:[email protected]>> wrote:
Some notes:
- Since you specified your kinematic relations as u = q',
then you should set your velocities with u instead of q, for
example: p1.set_vel(N, u1d * N.x)
- I doubt that you need to specify any velocity constraints
and thus you will not have any dependent speeds. You've
defined ell as some new coordinate, but do not add it as an
independent coordinate. I don't think this is correct. It
will likely work if you just remove the coordinate
constraint stuff.
Jason
moorepants.info <http://moorepants.info>
+01 530-601-9791 <tel:530-601-9791>
On Mon, Jan 12, 2015 at 5:12 AM, Guillaume Gay
<[email protected] <mailto:[email protected]>> wrote:
Hi,
I'm trying to use sympy KanesMethod to model biological
assemblies (i.e. the mitotic spindle).
Molecular motors in biology follow linear force velocity
relationships, such that F = F_max(1 -ld/V_max) where ld
is the relative speed of the two points on which the
force is applied (distant of l).
I strugle to implement this in the Kanes formalism... I
tried various things:
* constraint the generalized speed as u = (V_max - ld)
* declare the above relation in the kinetic differential
equation
In both cases, the `to_linearizer` method rises a:
ValueError: Cannot have dynamicsymbols outside dynamic
forcing vector.
* use directly ld as the speed, and declare it as auxiliary
Then I have a shape mismatch when I try to linearize.
Bellow is a notebook with the code:
http://nbviewer.ipython.org/github/glyg/Notebooks/blob/master/kt_sim/minimum%20Linear%20Force%20Velocity.ipynb
Best,
Guillaume
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http://damcb.com
43 rue Horace Bertin
13005 Marseille
+33 953 55 98 89
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