laplace transform of a product
laplace transform of a product
(OP)
Hello,
I realize that this is a silly question but I'm currently working on a control system for a robotic arm and I'm trying to compute a laplace transform for the following function:
cos(x)*x" + (x')^2 = y
in particular I'm having a problem with the laplace transform of a product of cos(x) and the 2nd derivative of x. also, I'm a bit puzzled by the square of the 1st derivative of x. Thank you very much for any help.
r.
I realize that this is a silly question but I'm currently working on a control system for a robotic arm and I'm trying to compute a laplace transform for the following function:
cos(x)*x" + (x')^2 = y
in particular I'm having a problem with the laplace transform of a product of cos(x) and the 2nd derivative of x. also, I'm a bit puzzled by the square of the 1st derivative of x. Thank you very much for any help.
r.





RE: laplace transform of a product
Sometimes you can get rid of the product through partial fraction expansion, but I don't think that will work here.
By the way, it's not clear to me the context of the equation. Is this a differential equation in x(t), where y(t) is an input/independent function?
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RE: laplace transform of a product
I'm writing the Langrangian equation for the motion of the arm that's where I get the product of the cosine and the 2nd derivative of the variable:
M(q)q” + V(q,q’) + G(q)= ?
? = d/dt(?L/??’) - (?L/??)
where '?' is the partial derivative. Also, here I have 'q' as my input and '?' as the output. But, for the simplicity, I originally used 'x' and 'y' and my input and output variables.
I tried just about everything, including MathCad, MatLab and even trying to derive the expression myself using the definition of Laplace Transform. But, so far, I am failing miserably. Thanks for your help.
r.
RE: laplace transform of a product
I strongly suggest that you present the problem as it appears so you can get a verification of that equation first. Then we can talk about a solution.
For example, for an arm falling freely ( a simple pendulum), I get
T=I/2*@'^2
V=Mgl/2*(1-cos(@))
L=T-V
And
d/dt part(L)/d@'-part(L)/d@=I@"+1/2Mglsin(@)=0