Curvature

10072022, 12:28 AM
Post: #1




Curvature
Gratitude to Arno K. and rombio for helping me with derivatives and CAS programs.
The following CAS functions calculates the curvature of: functions, y(x) polar functions, r(t) (t: Θ) parametric functions, x(t), y(t) Let Δα be the angle of rotation angle and Δs is the slight change of distance. Then the radius of curvature is: K = abs(Δα ÷ Δs) as Δs → 0 And the radius of curvature is the reciprocal of K. For circles, the radius of curvature is constant. Wankel engines and rotary engines have their pistons traveling in a circle. Calculating the curvature depends on the form of the function. Function: y(x) K = abs( y''(x) ) ÷ (1 + (y'(x))^2) ^(3/2) Polar: r(t) (t replaces Θ) K = abs( r(t)^2 + 2 * (r'(t))^2  r(t) * r''(t) ) ÷ ( r(t)^2 + r'(t)^2 )^(3/2) Parametric: x(t), y(t) K = abs( x'(t) * y''(t)  y'(t) * x''(t) ) ÷ ( x'(t)^2 + y'(t)^2 )^(3/2) Radius of Curvature: r = 1 ÷ K HP Prime CAS Program: crvfunc Code: #cas HP Prime CAS Program: crvpol Code: #cas HP Prime CAS Program: crvpar Code: #cas Source: Svirin, Alex Ph.D. "Curvature and Radius of Curvature" Math24 https://math24.net/curvatureradius.html 2022. Last Updated September 12, 2022. 

09242023, 08:21 AM
Post: #2




RE: Curvature
These programs seem to be having some trouble running. I'm getting the error (!) when I try to run them from the Program menu, and they simply don't pop up in the User>Program Functions list. I'm wondering if you might have a sec to trouble shoot?
Actions I've tried: Copied & pasted the exact text for each program via HP Connectivity Kit Attempted to locate the program using Catlg, calc displays 100% read only code Uninstalled & reinstalled programs Reset HP Prime via pinhole reset on back Hopefully I'm doing something wrong, and that something is obvious and you spot it easily so I can learn from the mistake. 

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