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Swinging damped pendulum system: parameters in body and damper

Posted 4 months ago
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Hi All, I am complete newbie to Wolfram System Modeler and have not had any training on the system. Trying to figure it out as I go.

I need to do simulation of pendulum on Wolfram System modeler. Model includes world, revolute with rotational damper and body. Revolute rotating on z-axis's. I was able to add body mass, distance from revolute(length of string) and start angle to the requires parameters in the model. I have 2 uncertainties:

1) I am not sure where I need to add the inertia in the model under the body. When selecting body in model, it shows the inertia tensor. Under inertia tensor the are I11, I22,I33...... Under which I ... do I need the add the inertia? See attached.

2) The damping force coefficient is a given as 0.00142 kg/s. When selecting damper in the model the damping constant unit is in Nms/rad. How do I convert or calculate kg/s to Nms/rad or is there a way to change the Nms/rad unit? See attached.

If any addition info are required, please let me know.

Thank you in advance for replies

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2 Replies

Hi Tiaan,

Let me answer first the second question.

The units that you have for that damping constant, 0.00142 kg/s, makes me think that you have a translational damping constant instead of a rotational damping constant. The latter is the one expected in the parameter d of the damper component. Assuming that this was not a typo, the most likely case here is that your value, 0.00142 kg/s, actually corresponds to d/l^2, where l is the distance from the pivot of your pendulum to the center of mass of the body, in meters. Hence, d = 0.00142 * l^2.

The first question has a couple of more nuanced details. When you look at the component Modelica.Mechanics.MultiBody.Parts.Body, you find that the parameters I_11, I_21, I_31, I_22, I_32, I_33 are the components of the parameter I, which is described, in the component, as the inertia tensor: I[3, 3] = [I_11, I_21, I_31; I_21, I_22, I_32; I_31, I_32, I_33]. If you go to the documentation of the component, you find

The inertia tensor has to be defined with respect to a coordinate system that is parallel to frame_a with the origin at the center of mass of the body.

So it is in this sense that you can read these values and you have to take this into account when plugging in the parameter values you were given.

To ground this discussion a bit, let me be more specific, using the parameter values that I can read from your attachments. You seem to have picked the axis of rotation of your revolute as n = {0, 0, 1}. Due to the constraint implicit in the single revolute component of the model, rotations around any other orthogonal axes are not allowed. The most likely case of interest is then the one in which I_31 = 0, I_32 = 0 and I_33 is the only non-vanishing component of interest, because this reduces your rotational dynamics to those of the standard physical pendulum. With that being clarified, the last thing you have to take into account is the fact that I_33 will correspond to the moment of inertia with respect to the center of mass, as mentioned in the documentation. If it turns out you were given instead the moment of inertia with respect to the pivot of the pendulum, you will have to use the parallel axis theorem to compute I_33.

Posted 4 months ago

Thanx for the info and help. Much appreciated.

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