Macaulay functions in MUPad

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Ed Davis
Ed Davis on 12 Nov 2014
In general the Macaulay function (<x-a>^n) is evaluated as 0 for x<a and x^n for x>a.
The integral is defined as int(<x-a>^n)=(<x-a>^(n+1))/(n+1)
I would like to implement functions of this type in MuPad to allow solving of beam deflection problems symbolically. However, I am not able to find a function that behaves as the Macaulay functions do. Any suggestions would be appreciated.
Nathan Hardenberg
Nathan Hardenberg on 3 Dec 2022
I did not solve the deflection problem, but I wrote a symbolic solver for shear force and bending moment. It is pretty well documented in the ReadMe file and you obviously can get some inspiration from the code.
I also found a Python implementation that should be able to symbolically calculate deflection, shear force etc. Having said this, I did not use it yet.

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Answers (1)

Nathan Hardenberg
Nathan Hardenberg on 29 May 2020
Not quite the solution you are looking for, but it is certainly possible to use the heaviside function. The heaviside function is also integratable and differentiable, so it is possible to use it instead.
<x - a>^0 is heaviside(x-a)
For functions with a higher exponent you have to write something like this
x^2 * heaviside(x-a)
this "switches" the function x^2 on (after a). Before it is 0
Nathan Hardenberg
Nathan Hardenberg on 6 Dec 2022
You are right in the fact, that is not !
But here < and > are meant as macaulay brackets. With this notation my statement is correct. See the equation here.
It's probably better written as equation:
But note that the term is not defined at . In MATLAB is defined as at this position. It is sometimes also defined as 1.

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