471f3fad-1df5-414b-9219-2f3781353897 9 15 12 decimal

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

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

V 20 :

a 50 :

b 100 :

ω V r / : 0.253

t 0 (8 (0.1 range :

n t length :

n 81

k 1 n range x k el 5050 ω t k el * π 2 / + sin * - (: y k el 100 ω t k el * sin * : 21 line for

t Clear 1

t x 501 ω t * π 2 / + sin - (* : t y 100 ω t * sin * : 21 sys

t x 501 ω t * π 2 / + sin - (* :

t y 100 ω t * sin * :

t c t x t diff t y t 2 diff * (t y t diff t x t 2 diff * (- (abs t x t diff (2^t y t diff (2^+ (32 /^/ :

x c

t R.c 1 t c / :

m 189 kg * :

t α b.G t R.c / atan :

h.G 0.53 m * :

I.xG 6.73 kg * m 2^* :

b.G 0.703 m * :

I.zG 36.4 kg * m 2^* :

p 1.42 m * :

t x' t x t diff :

t x' t x t diff : t y' t y t diff : t m t y' t x' / : t Δ π 2 / t m atan - (: t F.sf b.G p t Δ cos * / m * V 2^t R.c / * : 51 sys

t y' t y t diff :

t m t y' t x' / :

t Δ π 2 / t m atan - (:

t F.sf b.G p t Δ cos * / m * V 2^t R.c / * :

x x' x y' 2 1 sys x m x Δ x F.sf

I.xG m h.G 2^* + 59.8201 kg * m 2^*

m 189 kg *

Y2 I.xG m h.G 2^* + (: 59.8201 kg * m 2^*

This is a 2nd order DE
but undefined wrt  φ(t) t φ'' Y2 * m V 2^* h.G t R.c / * t φ cos * m 9.8 * h.G * t φ sin * - ≡

t t 2 diff Y2 *

t φ'

m V 2 ^ * h.G x R.c / *

m V 2^* h.G * 40068 kg m * *

m 9.8 * h.G * 981.666 kg * m *

DE variable coefficients term 2
Don't think it has solution whatsoever t φ'' f 1 el * f 2 el 1 t R.c / * t φ' cos * - f 3 el t φ' sin * + 0 ≡

f 59.8201 40068 981.666 31 sys :

x Y Clear 1

x y x 2 diff 3 x y x diff * + 7 x y * - 4 x * ≡

x0 0 : (start ≡ x1 1 : (end ≡ N 100 : (mesh ≡ 31 line

IC 1010 - 21 mat :

<= implies user initials =>
 ....... user choice ...... x Y D Y 2 el 3 Y 2 el * - 7 Y 1 el * + 4 x * + 21 mat :

Runge-Kutta-Fehlberg Method (RKF45). sol IC x0 x1 N x Y D Rkadapt :

x sol 1 col : X sol 2 col : Y sol 3 col : 31 line

U x X augment : V x Y augment : 31 line

U V 2 1 sys

m V 2^* h.G t R.c / * t φ cos * (m 9.8 * h.G * t φ sin * (- I.xG m h.G 2^* + (t φ'' * (- 0 :

t φ

m V 2^t R.c / * t α sin * (t F.sf t ψ sin * (- I.zG m b.G 2^* + (t ψ'' * (- 0 :

t ψ