Post Reply 
(50g) osculating circle
12-22-2015, 08:36 PM (This post was last modified: 06-26-2020 06:08 AM by peacecalc.)
Post: #1
(50g) osculating circle
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
Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: 1 Guest(s)