ACCEPTED SOLUTION
Accepted Solutions
OK, by now you should have learned two things:
1) Don't copy math expressions from a Prime sheet to your community post here - it gets unreadable
2) Its nice to post pictures, but the worksheet itself would be of much more value most of the time. So use the option to attach files here:
You stated which version of Prime you are using and that's good an necessary. Next time you may want to do this even more eye-catching at the front of your post.
According your Prime problem: You defined a function for jerk and the value you assign is a vector with 40 elements.
That means that the result value for any argument t of your function would be that whole vector. Obviously that's nothing Prime would be able to integrate - hence the error message you receive.
You have two options:
1) Use the trapezoid rule but work with the vectors of time and jerk values, not any functions:
2) Turn your data vectors into a function. The most obvious way is to use linear interpolation and Prime offers this out of the box with the function "linterp".
You may also use cubic spline interpolation which also offered by Prime, but I guess that this would not be appropriate in your case. Spline interpolations tends to a more "wavy" (sometimes overshooting), but smoother signal. It may have its use if you intend to use the derivative as it avoids the jumps in the derivative you otherwise get because of the sudden changes in slope.
Here you see the difference concerning the derivative. But while smother you have to be aware that cubic spline interpolation adds data information which actually is not there in the original data ...
Prime 10 worksheet attached
You should better attach the worksheet file, the .mcdx file.
Other than that. Your jerk_MH_N(t) is not a function, but a vector, and you cannot integrate a vector, but you can sum it:
And you can construct a curve through your datapoints, using linear interpolation or splines make that into a function and then integrate over that function.
Success!
Luc
OK, by now you should have learned two things:
1) Don't copy math expressions from a Prime sheet to your community post here - it gets unreadable
2) Its nice to post pictures, but the worksheet itself would be of much more value most of the time. So use the option to attach files here:
You stated which version of Prime you are using and that's good an necessary. Next time you may want to do this even more eye-catching at the front of your post.
According your Prime problem: You defined a function for jerk and the value you assign is a vector with 40 elements.
That means that the result value for any argument t of your function would be that whole vector. Obviously that's nothing Prime would be able to integrate - hence the error message you receive.
You have two options:
1) Use the trapezoid rule but work with the vectors of time and jerk values, not any functions:
2) Turn your data vectors into a function. The most obvious way is to use linear interpolation and Prime offers this out of the box with the function "linterp".
You may also use cubic spline interpolation which also offered by Prime, but I guess that this would not be appropriate in your case. Spline interpolations tends to a more "wavy" (sometimes overshooting), but smoother signal. It may have its use if you intend to use the derivative as it avoids the jumps in the derivative you otherwise get because of the sudden changes in slope.
Here you see the difference concerning the derivative. But while smother you have to be aware that cubic spline interpolation adds data information which actually is not there in the original data ...
Prime 10 worksheet attached
Your sheet isn't showing any derivatives but a lot of errors we already fixed in my previous answer!
jerk_MH_N is a vector, so don't define it as if it were a function.
Not sure what you tried when you evaluated jerk_fun_MH_N(t). t is a vector of just 40 values, so you get a result vector with the 40 corresponding values which should be exact the vector jerk_MH_N.
So to see the smoothing effect of the spline interpolation you would rather define a range (just for plotting!) with a much smaller step size:
Next problem:
1) "time" is a vector with 40 integer values (its the same as vector t). The limit of an integral can't be a vector, it has to be a scalar
2) interpolation is a numeric only process. You can't symbolically evaluate an expression which uses a function derived by numeric evaluation
Maybe you meant
This defines a function which can be (numerically) evaluated at any position
or plotted, if you like
Calculating 40 values takes 15 minutes? So I would suggest you don't try to plot the last integration function because this would mean evaluating it at much more than 40 positions.
By all your calculations you should never forget that all are just based on 40 discrete input values, which is not really a lot.
BTW, you can speed up the calculation significally if you predefine the vector which is the first argument when calling "interp". That way this vector must not be calculated from anew every time the function is evaluated:
I am now to try the trapeze rules for numerical integration.
Did have the MP10 any numerical function for trapeze, Simpson or other integration numerical formulas?
I guess that the numerical integration in Prime is using kind of a modified Simpson or the like.
But of course you can't expect any analytical, symbolical results from numerical methods.
So if you use linear interpolation you should get 'exact' results as with the trapezoid rule.
Keep in mind that numerical integration may take a long time.
This is especially true when it comes to plotting at a dense grid and the nested double integration as in function "vel":
I could not wait for vel(tt) finishing its calculations 😉
OK, i went away when when I came back after quite some time the pot had finished.
It looks like the numeric integral was not converging at some positions where the plot shows gaps.
Here is one position where the integration fails
Sometimes it helps to set the system variable TOL to a lower value (default is 10^-3) for a higher precision, but at the cost of an even increasing calculation time
