Modelling Foucault's pendulum attached to a cylindrical disk in Simscape Multibody

Hi,

I am trying to model a spinning disk attached to a rod in simscape multibody, as shown in the diagram attached. The disk is supposed to spin at a constant rate and cause the pendulum trajectory to shift, as opposed to going back and forth. The rod does not spin on its own axis. Please see this https://www.youtube.com/watch?v=pKGgICawAKc as an example of what I am trying to model, but note that I have a spinning disk instead of a spinning sphere.

I have also attached a draft of the model, but it doesn't seem to work correctly since I cannot see the pendulum behaviour and both the rod and disk are spinning along the vertical axis. Could you please help introduce correct translational behaviour into the system or share any similar models you may have done?

Thank you for your help.

Answer 1

[Steve Miller]

Hi Jake - attached to this answer is a model I built that I believe models the system you describe. Please note the location of the sensor and the frame used to define the camera. They are both in the reference frame that is spinning.

--Steve

[Jake Barlow]

Hi Steve, this is brilliant. Thank you very much. I will have a look at it in more detail, but just a few questions. Is pend.init.bob_x the initial displacement of the bob in the x-direction and pend.eve.w the angular frequency? For the former, could you please let me know where I can change the initial displacement in the y-direction as well?

[Steve Miller]

Hi Jake,

• pend.init.bob_x Initial displacement of the bob in the x-direction
• pend.env.w the angular speed of the disk upon which the pendulum sits.

You can set the initial positions in the Universal Joint.

[Jake Barlow]

Hi Steve, thank you for the clarifications. I will look into the model further and let you know if I have more questions. Thank you very much for your help!

[Jake Barlow]

Hi Steve, I tried to test the model for the case when the angular speed and rpm of the disk are both zero, so that we have a simple pendulum. However after setting the the initial velocity in the x-direction to be 1 and the

remaining initial conditions to be zero, as shown below:

I get the following trajectory

So it seems that the x and y coordinates are switched around. Also after setting the initial conditions

I get this graph:

which again looks like the x and y coordinates are switched around. Since both the initial velocities in the x and y directions are positive, their trajectory should be on the line y=x (instead of y=-x as shown above).

Could you please help me with this? Thank you.

[Steve Miller]

The velocities you are setting are not translation along the x- and y- axes, they are the rotational speeds about the degrees of freedom about the x- and y- axes of the joint. If the pendulum rotates about the x axis, you get velocity along the y axis.

--Steve

[Jake Barlow]

Hi Steve, thank you for the reply. Is there a way to set linear speeds instead of rotational speeds in simscape? Or something similar for large angles of rotations from the vertical axis? Thank you.

[Steve Miller]

The tip of the pendulum has to follow an arc. If you want to specify the linear speed of the tip of the pendulum, you need to figure out how fast the pendulum needs to be rotating about its two DOFs to achieve that linear speed (which must be within a plane normal to the pendulum rod) and set the rotational speeds there. The calculation is trivial if the pendulum is pointing straight down, slightly more complex if it starts at an initial angle.

[Jake Barlow]

Hi Steve, thank you very much for your replies. So for very small initial angles, am I correct in suggesting that the linear speed in the horizontal plane can be taken to be the resultant of the rotational speeds in the x and y directions?

If I want to make comparisons with a simple pendulum trajectory, that is, no spinning disk or rod, then it will be difficult to set the simscape initial velocities in rad/s or deg/s or rpm since a pendulum 2D system moves in a plane with no rotations along its vertical axis and angular momentum is not conserved due to gravity.