a0e112fd-4790-4513-9f49-0a830a098cd8 9 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

V 20 :

a 50 :

b 100 :

r a 2^b 2^+ 2 / (12 /^:

ω V r / : 0.253

t x 5050 ω t * π 2 / + sin * - : t y 100 ω t * sin * : 21 sys

T 08 0.01 range :

k 1 T rows range :

You can use uppercase for vectors. Even k it's one, it's more than a counter.

With index

X k el T k el x eval : Y k el T k el y eval : 21 sys

M X Y augment :

M M rows row 71.886 89.9111 12 mat

With vectorize

X T x vectorize eval : Y T y vectorize eval : 21 sys

M X Y augment :

M M rows row 71.886 89.9111 12 mat

dy dx / dy dt / dt dx / * ≡

Point P

t.P 3 :

x.P y.P 21 mat t.P x t.P y 21 mat :

y dy dx / x x.P - (* y.P + ≡

Derivatives

t x' t x t diff :

t y' t y t diff :

t x'' t x' t diff :

t y'' t y' t diff :

Tangent

m t.P y' t.P x' / :

tg k el m X k el x.P - (* y.P + eval :

tg m T x x.P - (* y.P + vectorize eval :

x tg m x x.P - (* y.P + :

and plot it as tg(x)

t c t x' t y'' * t y' t x'' * - t x' 2^t y' 2^+ (3^sqrt / :

The curvature have sign.

x.C y.C 21 mat x.P y.P 21 mat 1 t.P c t.P x' t.P y' 21 mat norme * / t.P y' - t.P x' 21 mat * + : 107.2946 24.4413 21 mat

Center of Osculating Circle

XO YO 12 mat T cos t.P c abs / x.C + vectorize T sin t.P c abs / y.C + vectorize 12 mat eval :

x 0 > ( x 8 < ( & x c not defined if M x tg XO YO augment x.C y.C x.P y.P 2 2 mat x.P y.P o 10 red augment x.C y.C o 10 green augment 6 1 sys