x(t)

A_t

Start

x(t)

x

x'

x''=\sqrt{1+(x')^2}

Mitte Hyperbel

t

N

Start = (0.6044560867449071, -0.5825136552917674)
a: x(Start)
b: y(Start)
fk(x) = a - (sqrt(1 + b^(2)) * (1 - cosh(x))) + (b * sinh(x))
fk'(x) = fk'(x)
S = Intersect(fk', xAxis, (0.5537727653501717, 0))
xmin = -6 (slider from -10 to 15, step 1)
xmax = 10 (slider from -10 to 15, step 1)
ymin = -6 (slider from -10 to 15, step 1)
ymax = 6 (slider from -10 to 15, step 1)
mm = Sequence(Sequence[If[yy > 0, atan(sqrt(1 + 100 / yy^(2))), atan((-sqrt(1 + 100 / yy^(2)))) + π], xx, xmin, xmax], yy, ymin, ymax)
rr = 0.28 (slider from -5 to 5, step 0.01)
phi = 0.7235987755982988 (slider from -5 to 5, step 0.1)
B = (-6, 5)
C = (-6, -5)
t = 0.83 (slider from 0 to 1, step 0.01)
Fk: (t - 6, fk(t - 6))
ll = Sequence(Sequence[sqrt(1 + (0.02 * yy^(2))), xx, xmin, xmax], yy, ymin, ymax)
Richtungsfeld = Sequence(Sequence[Vector[(i / 10, j / 10), (i / 10 + (((0.2 * rr) * Element[Element[ll, j - ymin + 1], i - xmin + 1]) * cos(Element[Element[mm, j - ymin + 1], i - xmin + 1])), j / 10 + (((0.2 * rr) * Element[Element[ll, j - ymin + 1], i - xmin + 1]) * sin(Element[Element[mm, j - ymin + 1], i - xmin + 1])))], i, xmin, xmax], j, ymin, ymax)
A: (t, x(Start) - (sqrt(1 + (y(Start))^(2)) * (1 - cosh(t))) + (y(Start) * sinh(t)))
AA: (x(Start) - cosh(asinh(y(Start))) + cosh(t + asinh(y(Start))), sinh(t + asinh(y(Start))))
Ks = CurveCartesian(x(Start) - cosh(asinh(y(Start))) + cosh(t + asinh(y(Start))), sinh(t + asinh(y(Start))), t, 0, 1.36)
H: (0, x(Start))
Mhyp: (x(Start) - sqrt(1 + (y(Start))^(2)), 0)
c: fk'(0)
h: y = 0.6 + (c * x)
m = OrthogonalLine(A, xAxis)
M = Intersect(m, xAxis)
n = Segment(A, M)
q = OrthogonalLine(AA, yAxis)
P = Intersect(q, yAxis)
r = Segment(P, AA)
N = Intersect(xAxis, Ks)
O: (0, 0)
p = Segment(O, N)
s = OrthogonalLine(S, xAxis)
R = Intersect(fk, s, (0.5537727653501717, 0.44716521639235124))
f_1 = Segment(R, S)
D = (0.3114552030713186, -0.2249735156047604)
E = (0.6539733683572477, -0.22606798935263092)
F = (0.31145520307131863, -0.04547982095400868)