Solution $y(x)$ for $-cos(x)= int_0^{2pi}max(y(t), y(x+t))dt$
$begingroup$
The application here is to design a value which will produce a sine wave like pressure or flow rate as a function of time. Pressure, or flow rate is a function of the open area inside of a valve. The open area is a function of the area of two identical cams placed back to back in the valve body rotating relative to each other. As the two cams rotate, the combined area of the two cams need to create a sine wave area function vs time. A little thought should convince you that the way to combine the area from the two cams is the max() function.
So I give you:
$ -cos(x) = int_0^{2pi}max(y(t),y(x+t))dt$
I seek $y(x)$ which is the contour of the two identical cams. I was also told that:
$ max(a,b) = frac{(a+b + |a-b|)}{2}$
* Note: I asked this question a few day ago but I was encouraged to abandon that question and start a new one because I change the LHS from sin(x) to -cos(x). I changed the LHS from sin(x) to -cos(x) because it was shown that sin(x) does not have a solution.
integration analysis integral-equations
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
$endgroup$
add a comment |
$begingroup$
The application here is to design a value which will produce a sine wave like pressure or flow rate as a function of time. Pressure, or flow rate is a function of the open area inside of a valve. The open area is a function of the area of two identical cams placed back to back in the valve body rotating relative to each other. As the two cams rotate, the combined area of the two cams need to create a sine wave area function vs time. A little thought should convince you that the way to combine the area from the two cams is the max() function.
So I give you:
$ -cos(x) = int_0^{2pi}max(y(t),y(x+t))dt$
I seek $y(x)$ which is the contour of the two identical cams. I was also told that:
$ max(a,b) = frac{(a+b + |a-b|)}{2}$
* Note: I asked this question a few day ago but I was encouraged to abandon that question and start a new one because I change the LHS from sin(x) to -cos(x). I changed the LHS from sin(x) to -cos(x) because it was shown that sin(x) does not have a solution.
integration analysis integral-equations
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
$endgroup$
add a comment |
$begingroup$
The application here is to design a value which will produce a sine wave like pressure or flow rate as a function of time. Pressure, or flow rate is a function of the open area inside of a valve. The open area is a function of the area of two identical cams placed back to back in the valve body rotating relative to each other. As the two cams rotate, the combined area of the two cams need to create a sine wave area function vs time. A little thought should convince you that the way to combine the area from the two cams is the max() function.
So I give you:
$ -cos(x) = int_0^{2pi}max(y(t),y(x+t))dt$
I seek $y(x)$ which is the contour of the two identical cams. I was also told that:
$ max(a,b) = frac{(a+b + |a-b|)}{2}$
* Note: I asked this question a few day ago but I was encouraged to abandon that question and start a new one because I change the LHS from sin(x) to -cos(x). I changed the LHS from sin(x) to -cos(x) because it was shown that sin(x) does not have a solution.
integration analysis integral-equations
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
$endgroup$
The application here is to design a value which will produce a sine wave like pressure or flow rate as a function of time. Pressure, or flow rate is a function of the open area inside of a valve. The open area is a function of the area of two identical cams placed back to back in the valve body rotating relative to each other. As the two cams rotate, the combined area of the two cams need to create a sine wave area function vs time. A little thought should convince you that the way to combine the area from the two cams is the max() function.
So I give you:
$ -cos(x) = int_0^{2pi}max(y(t),y(x+t))dt$
I seek $y(x)$ which is the contour of the two identical cams. I was also told that:
$ max(a,b) = frac{(a+b + |a-b|)}{2}$
* Note: I asked this question a few day ago but I was encouraged to abandon that question and start a new one because I change the LHS from sin(x) to -cos(x). I changed the LHS from sin(x) to -cos(x) because it was shown that sin(x) does not have a solution.
integration analysis integral-equations
integration analysis integral-equations
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
edited Dec 10 '18 at 23:11
Jeffery Stout
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
asked Dec 10 '18 at 23:05
Jeffery StoutJeffery Stout
343
343
add a comment |
add a comment |
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