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+--- Thread: (50g) osculating circle (/thread-5392.html)
(50g) osculating circle - peacecalc - 12-22-2015 08:36 PM
Hello all,
The power of the HP 50g can be seen in that little program for calculating the coordinates of the center of the osculating circle and the radius r for 2-dimensional plane slopes. Which can be described by functions. The function is defined in the variable "FN".
I used the formulas:
\[ x_M = x - f'(x)\cdot\frac{1+ f'(x)^2}{f''(x)} \]
\[ y_M = f(x) + \frac{1+ f'(x)^2}{f''(x)} \]
\[ r = \frac{\sqrt{1+ f'(x)^2}^3}{f''(x)} \]
Code:
%%HP: T(3)A(R)F(,);
\<< 'X' 0 DUPDUP @@intial values
\-> X0 F0 F1 F2 @@for this variables
\<< X0 FN DUP @@the function f is defined in "FN"
'F0' STO @@the symbolic term of f is stored
@@F0
DERVX DUP @@first derivate is stored
'F1' STO @@in F1
DERVX @@second derivate is stored
'F2' STO @@in F2
F1 SQ 1 + DUP F2 / DUP @@calculating x-coordinate
F1 * NEG X0 + @@curvature circle
SIMPLIFY "XM" \->TAG
SWAP F0 + @@calculating y-coordinate
SIMPLIFY "YM" \->TAG @@curvature circle
ROT '3/2' ^ F2 / ABS @@calculating radius r of
"R" \->TAG @@ curvature circle
\>>
\>>For example: FN contains \<< \-> X \<< X 2 ^ \>> \>> you get as result:
\[ XM:\ \ - (4*X^3) \]
\[ YM:\ \ \frac{6*X^2+1}{2} \]
\[ R:\ \ \frac{\sqrt{4*X^2+1}^3}{2} \]
Feel free and enjoy the little program!
Every constructive critics or suggestions for improvement are welcome.
Greetings peacecalc