How can I measure the 3rd and 4th derivatives?

Measuring 3rd and 4th derivatives

Although most of us are content with measuring just the 1st and 2nd derivatives, some hard-core engineers may need to measure the 3rd and 4th derivatives (the jerk, and the jounce, respectively) of the position of a body.

Here is a neat trick that you can apply in Working Model Motion to get this information. In fact, if you apply this trick in series, you will be able to take as many derivatives of the position as you want.

Here’s how to do it:

  1. Create a meter plotting the acceleration of the body.
  2. Double-click the meter to view its Properties window. Select the Meter tab and notice the formulas that are used to plot the x, y, z components of the acceleration, as well as the magnitude of the acceleration. For example, the formula for the magnitude of the acceleration of body[1] will be: mag(body[1].a) Highlight the formula for the magnitude of the acceleration of the body and Copy it.
  3. Create a new body and attach a motor to this body. Double-click the motor to view its Properties page, select the Motor tab, and make the motor an Orientation motor. Paste the formula for the magnitude of the acceleration of body[1] into the orientation motor Value box. (Now you have an orientation motor whose output is the acceleration of body[1]).
  4. Create a meter measuring the angular velocity of this orientation motor. This will be the 1st derivative of the orientation motor, and the 3rd derivative of the position of the body.
  5. Create a meter measuring the angular acceleration of the orientation motor. This will be the 2nd derivative of the orientation motor, and the 4th derivative of the position of the body.

Note: When you create these meters, you will get a message telling you that "a specified motion or an applied force or torque depends directly or indirectly on the acceleration of body[1]." This is normal and will not affect the outcome of this particular calculation (double-click on the message for more information if you are inter-ested). Just click "Clear" and you’ll be on your way.

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Versioni pertinenti:

Working Model 2D, visualNastran 3D Motion, 4d, SimWise

Data ultimo aggiornamento: 2 settembre 2011



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