How do I compute jerk in 2D space for a mouse tracking task?

In summary: If not, can you give an example of a real world situation where jerk might be important?In summary, the researcher is trying to calculate the kinematics of a mouse tracking task, but is having difficulty understanding the formulas due to a lack of background in physics. She is seeking advice on how to calculate the derivatives of position, jerk, and acceleration.
  • #1
YoYojimbo
2
0
Hi everyone,

I am a graduate student in psychology and am working on a research project where I am trying to derive the kinematics of a mouse tracking task. I am currently writing a MATLAB script to do this, and I believe my equations for velocity and acceleration are correct, but I have very little background in physics/calculus and am having difficulty computing the 3rd derivative of position, jerk. I know this forum is for high school/undergraduate level students, but I believe this question is too simple to post in the other forum.

1. Homework Statement

I have calculated the euclidean distances between all xy samples and determined the sum of the euclidean distances to determine displacement for the entire movement and the displacement between each pair of xy coordinates.

With displacement:
I have calculated the average velocity with the formula "sum of euclidean distance/total time of movement.

I have calculated the velocity profile using the the euclidean distances between each pair of xy coordinates divided by the sample rate (the time between each sample, so .5ms).
In regards to calculating acceleration, I have used the same formulas as above, but replaced displacement with velocity (the rate of change of velocity)

However, in regards to jerk (the rate of change of acceleration), I am trying to make sure I am calculating this correctly. I keep finding different formulas, but I am not certain all of them apply to 2D kinematics. If jerk is the rate of change of acceleration, am I wrong in thinking it can be calculated by acceleration divided by the time between each xy coordinate pairs?

I think my main issue is digesting the formulas. I have read quite a bit about calculating the derivatives of position, but with my limited understanding of physics, it is difficult to determine if the formulas are applicable to above mentioned 2D coordinate plane situation.

I really appreciate the any advice/help anyone can offer!

Best
 
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  • #2
The only difference between 2D and "1D" Kinematics is you have x and y components. So anything that applies to 1 dimension should easily apply to 2 with the help of a little trig and geometry. What different formulas are your getting?
 
  • #3
Hi,

Thank you for the reply! I am using the following formulas.
upload_2015-1-30_11-2-5.png

upload_2015-1-30_11-2-26.png

upload_2015-1-30_11-2-45.png


Here are the jerk formulas
upload_2015-1-30_11-3-18.png

I assume this is the same as above
upload_2015-1-30_11-6-34.png

Those are the formulas I have found. The rest of the confusion comes from journal articles talking about jerk of arm movements. I am not sure if that is applicable to my situation. Does it seem like my thinking about the variables is correct?

Thank you.
 

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  • #4
YoYojimbo said:
Hi,

Thank you for the reply! I am using the following formulas.
View attachment 78416
View attachment 78417
View attachment 78418

Here are the jerk formulas
View attachment 78419
I assume this is the same as above
View attachment 78421
Those are the formulas I have found. The rest of the confusion comes from journal articles talking about jerk of arm movements. I am not sure if that is applicable to my situation. Does it seem like my thinking about the variables is correct?

Thank you.
That all looks ok, though I advise caution when dealing with real data. Each step in the differentiation chain can turn small errors into larger ones. You could apply some smoothing, but if overdone that will understate the values. You need to be aware of the precision of the original data and what that says about the answers.
You mention conflicting information regarding jerk of arms, but don't indicate what the conflict is. Is it possible those are not using "jerk" in this formal sense?
 
  • #5
regards,Hello, as a scientist, I can provide some guidance on computing jerk in 2D space. First of all, it is important to note that jerk is the third derivative of position, so it is the rate of change of acceleration. In order to calculate jerk, you will need to have data for both acceleration and time.

From your description, it seems like you have already correctly calculated displacement and velocity. To calculate acceleration, you will need to take the derivative of velocity with respect to time. This can be done using the formula: a = (v2-v1)/(t2-t1), where v2 and v1 are the velocities at two different times (t2 and t1).

Once you have calculated acceleration, you can then calculate jerk by taking the derivative of acceleration with respect to time. This can be done using the formula: j = (a2-a1)/(t2-t1), where a2 and a1 are the accelerations at two different times (t2 and t1).

In summary, to calculate jerk in 2D space, you will need to take the derivative of acceleration with respect to time. It is important to note that the formulas for derivatives are applicable in both 1D and 2D situations, so the formulas you have read should be applicable to your problem.

I hope this helps and good luck with your research project!
 

1. What is computing jerk in 2D space?

Computing jerk in 2D space refers to calculating the rate of change of acceleration over time in a two-dimensional coordinate system. It is a measure of how quickly the acceleration is changing in both the x and y directions.

2. Why is computing jerk important?

Computing jerk is important because it provides valuable information about the movement of an object. It can help us understand the acceleration patterns and predict future movements, which is crucial in fields such as physics, engineering, and robotics.

3. How is computing jerk calculated?

To calculate jerk, we first need to determine the acceleration in both the x and y directions. Then, we use the formula jerk = (change in acceleration)/(change in time). This will give us the average jerk over a specific time interval.

4. What are some real-world applications of computing jerk in 2D space?

Computing jerk in 2D space has various real-world applications. It is used in sports analytics to analyze the performance of athletes and improve their training. It is also used in robotics to control the movement of robots and ensure precise and smooth motion.

5. Are there any limitations or challenges when computing jerk in 2D space?

One of the main limitations of computing jerk in 2D space is that it assumes constant acceleration over the given time interval. In real-world scenarios, this may not always be the case. Additionally, accurately measuring acceleration in the x and y directions can be challenging and may require specialized equipment.

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