5650170e-fa42-4feb-9e97-a87709b18c29 10 3 5 false false 0 decimal

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

Federpendel

E.k 12 / m * v.x 2^v.y 2^+ (* :

Kinetische Energie

E.p m g * y * 12 / c * x 2^y 2^+ sqrt l.0 - (2^* + :

Potenzielle Energie

Lagrangesche Gleichungen 2. Art

E.k E.p - (q i el t diff diff t diff E.k E.p - (q i el diff - 0 ≡

l.0 1 :

m 1 :

c 20 :

g 10 :

n 200 :

t.e 10 :

L t x t y 2 1 mat t.e n Rkadapt :

x'' m * E.k E.p - (x diff ≡

y'' m * E.k E.p - (y diff ≡

0 x 1 ≡

0 x' 0 ≡

0 y 1 - ≡

0 y' 0 ≡

Umformen in DGL-System erster Ordung

X x v.x y v.y 41 mat ≡

t X D X 2 el X 1 el l.0 - X 1 el 2^X 3 el 2^+ sqrt + (* c * m X 1 el (2^X 3 el (2^+ sqrt * / - X 4 el g - X 3 el l.0 - X 1 el 2^X 3 el 2^+ sqrt + (* c * X 1 el 2^X 3 el 2^+ sqrt / - 41 mat :

X.0 101 - 041 mat :

Integration mit Runge-Kutta-Verfahren

l.0 1 :

m 1 :

c 20 :

g 10 :

n 200 :

k 1 n range :

L X.0 010 n X t D rkfixed :

L 2 col L 4 col augment L t 2 el L t 4 el . 20 red 1 5 mat L t 2 el L t 4 el 0 0 2 2 mat 3 1 sys

L 0101 - 0 0.05 0.993 0.292 - 1.01 - 0.207 - 0.1 0.971 0.578 - 1.02 - 0.412 - 0.15 0.935 0.854 - 1.05 - 0.614 - 0.2 0.886 1.11 - 1.08 - 0.81 - 0.25 0.824 1.36 - 1.13 - 1 - 0.3 0.75 1.58 - 1.18 - 1.17 - 0.35 0.666 1.79 - 1.24 - 1.32 - 0.4 0.572 1.97 - 1.31 - 1.44 - 95 mat