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:
\[ x_M = x - f'(x)\cdot\frac{1+ f'(x)^2}{f''(x)} \]
\[ y_M = f(x) + \frac{1+ f'(x)^2}{f''(x)} \]
\[ r = \frac{\sqrt{1+ f'(x)^2}^3}{f''(x)} \]
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
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