x

y

x = 3

Ha 2016

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 8.4.2.4: S. 253
www.kurven-erkunden-und-verstehen.de

Ha 2016

Lissajous-Krone 2-5

Grafik 2 und
3D ansehen

om_1 = 2
om_2 = 5
ph_1 = 0 (slider from -5 to 5, step π / 30)
ph_2 = 0
a_1 = 3
a_2 = 1
end = 2.7
t = 2.8 (slider from 0 to 20, step 0.1)
d = CurveCartesian((a_1 * sin((om_1 * t) + ph_1)), (a_2 * sin((om_2 * t) + 3)), t, 0, (end * π))
g(x) = (a_2 * sin((om_2 * x) - ph_2))
f(x) = (a_1 * sin((om_1 * x) - ph_1))
e = CurveCartesian((a_1 * sin((om_1 * t) - ph_1)), (a_2 * sin((om_2 * t) - ph_2)), t, (end * π / 2), (end * π))
a = CurveCartesian((a_1 * sin((om_1 * t) - ph_1)), (a_2 * sin((om_2 * t) - ph_2)), t, 0, (2 * π / 3))
b = CurveCartesian((a_1 * sin((om_1 * t) - ph_1)), (a_2 * sin((om_2 * t) - ph_2)), t, (2 * π / 3), (4 * π / 3))
c = CurveCartesian((a_1 * sin((om_1 * t) - ph_1)), (a_2 * sin((om_2 * t) - ph_2)), t, (4 / 3 * π), (2 * π))
h: y = 3
l: y = -3
P_x: (t, f(t))
P_y: (t, g(t))
m = Segment(P_x, P_y)
n = Segment((0, 0), (t, 0))
i = CurveCartesian((3 * cos((om_1 * t) - ph_1)), (3 * sin((om_1 * t) - ph_1)), sin((om_2 * t) - ph_2), t, 0, (2 * π / 3))
o = CurveCartesian((3 * cos((om_1 * t) - ph_1)), (3 * sin((om_1 * t) - ph_1)), sin((om_2 * t) - ph_2), t, 0, (2 * π))
j = CurveCartesian((3 * cos((om_1 * t) - ph_1)), (3 * sin((om_1 * t) - ph_1)), sin((om_2 * t) - ph_2), t, (2 * π / 3), (4 * π / 3))
k = CurveCartesian((3 * cos((om_1 * t) - ph_1)), (3 * sin((om_1 * t) - ph_1)), sin((om_2 * t) - ph_2), t, (4 * π / 3), (2 * π))
P_t: ((3 * cos((om_1 * t) - ph_1)), (3 * sin((om_1 * t) - ph_1)), sin((om_2 * t)))
P: ((3 * sin((om_1 * t) - ph_1)), sin((om_2 * t) - ph_2))
p = Segment((t, 0), P_x)
q = false