Solving an Integration Error with Acceleration Data

[mark2468]

Hi.

I have a set of data representing acceleration. To get the distance I integrate twice using a summation method and looks like:

accelleration: 0, 40, 30, -50,-80, -40.
velocity: 0, 40, 70, 20, -60, -100.
distance: 0, 40, 110, 130, 70, -30.

The distance should be zero as the movement goes back to the original point so there clearly is an error. Is there a better way to get the distance. I have heard runge kutta is good for this sort of stuff but am not sure where and how to put the data in. Any suggestions to how i can sort out this error.

Thanks.

Mark.

 

[berkeman]

Hi.

I have a set of data representing acceleration. To get the distance I integrate twice using a summation method and looks like:

accelleration: 0, 40, 30, -50,-80, -40.
velocity: 0, 40, 70, 20, -60, -100.
distance: 0, 40, 110, 130, 70, -30.

The distance should be zero as the movement goes back to the original point so there clearly is an error. Is there a better way to get the distance. I have heard runge kutta is good for this sort of stuff but am not sure where and how to put the data in. Any suggestions to how i can sort out this error.

Thanks.

Mark.

Can you include time information in your dataset? What are the time intervals?

 

[mark2468]

time intervals are 0.333 seconds.

 

[berkeman]

time intervals are 0.333 seconds.

If your acceleration is 40m/s^2 for 1/3 of a second, you are not going 40m/s at the end of that time interval...

 

[Strants]

time intervals are 0.333 seconds.

And is the acceleration in units per second^2? If so, haven't you got the wrong values for velocity, as the time intervals were less than a second?

EDIT: missed berkeman's post, sorry

 

[ehild]

Apart from the length of the time interval, the displacement during a time interval Δt is the average velocity multiplied by Δt. In the first interval it is 20 (Δt)², and the total displacement is the sum of all the individual displacements.

ehild

 

[mark2468]

So what is the best way to synchronise them. Is there a formula or just divide by that ammout. e.g. 40/3, 30/3 etc or whatever the sample interval is. Any links with examples of this available?

Thanks again.

 

[ehild]

Assuming constant acceleration during a time interval Δt, the displacement during Δt is

d=(v(initial)+v(final))/2 *Δt.

ehild