Lissajousovy obrazce
Date: 5 Říjen 2013

Lissajousovy obrazce

Křivka

Malý náhled

Stopa

Smazat stopu = Ctrl+F

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t = 0

Start - Stop

Δφ = 0 (slider from 0 to 360, step 15)
ω_x = 1 (slider from 1 to 20, step 1)
ω_y = 2 (slider from 1 to 20, step 1)
t = 0 (slider from 0 to 6.283185307179586, step 1.0E-4)
A_1: (sin(ω_x * t), sin(ω_y * t + Δφ * π / 180))
B_1: (0, sin(ω_y * t + Δφ * π / 180))
C: (sin(ω_x * t), 0)
b = Segment(A_1, B_1)
c = Segment(A_1, C)
f = Polynomial({(1, -1), (1, 1), (-1, 1), (-1, -1)})
text1 = FractionText(ω_x / ω_y)
d = false
g = false
D = (-1.618543908374668, -0.6362051282928071)
h = Segment((-1, 0), (1, 0))
i = Segment((0, -1), (0, 1))
j = Segment((-1, -1), (1, -1))
k = Segment((-1, 1), (1, 1))
l = Segment((-1, -1), (-1, 1))
m = Segment((1, -1), (1, 1))
n = false
delta: Δφ * 180 / π
AA: (sin(ω_x * t), sin(ω_y * t + Δφ * π / 180))
E = (2.2, 0)
p = Circle(E, 1)
B: (2.2 + cos(ω_y * t + Δφ * π / 180), sin(ω_y * t + Δφ * π / 180))
q = Segment(AA, B)
u = Vector(E, B)
H = (0, -2.2)
r = Circle(H, 1)
A: (sin(ω_x * t), -2.2 - cos(ω_x * t))
s = Segment(C, A)
v = Vector(H, A)
a = CurveCartesian(sin(ω_x * t), sin(ω_y * t + Δφ * π / 180), t, 0, 12.56637)
e = CurveCartesian(0.35 * sin(ω_x * t) + x(D), 0.35 * sin(ω_y * t + Δφ * π / 180) + y(D), t, 0, 12.56637)
J: (x(E) + 1, 0)
J' = Rotate(J, 15*°, E)
J'_1 = Rotate(J, 30*°, E)
J'_2 = Rotate(J, 45*°, E)
J'_3 = Rotate(J, 60*°, E)
J'_4 = Rotate(J, 75*°, E)
J'_5 = Rotate(J, 90*°, E)
J'_6 = Rotate(J, 105*°, E)
J'_7 = Rotate(J, 120*°, E)
J'_8 = Rotate(J, 135*°, E)
J'_9 = Rotate(J, 150*°, E)
J'_{10} = Rotate(J, 165*°, E)
J'_{11} = Rotate(J, 180*°, E)
J'_{12} = Rotate(J, 195*°, E)
J'_{13} = Rotate(J, 210*°, E)
J'_{14} = Rotate(J, 225*°, E)
J'_{15} = Rotate(J, 240*°, E)
J'_{16} = Rotate(J, 255*°, E)
J'_{17} = Rotate(J, 270*°, E)
J'_{18} = Rotate(J, 285*°, E)
J'_{19} = Rotate(J, 300*°, E)
J'_{20} = Rotate(J, 315*°, E)
J'_{21} = Rotate(J, 330*°, E)
J'_{22} = Rotate(J, 345*°, E)
t_1 = Segment(J'_{11}, J)
a_1 = Segment(J'_5, J'_{17})
K = (0, -3.2)
K' = Rotate(K, 90*°, H)
K'_1 = Rotate(K, 180*°, H)
K'_2 = Rotate(K, 270*°, H)
w = Vector(E, Rotate[J, Δφ°, E])
b_1 = Segment(K'_2, K')
c_1 = Segment(K'_1, K)
time = 0
ma = 0
G: (20, ω_x + ω_y + Δφ + n + ma)
on = 0
anim = 0.46 (slider from 0.01 to 1.5, step 0.01)
text2: " \frac{ ω_x }{ω_y }\;=   " + (LaTeX[text1]) + ""
F = (1.2589833460111597, -1.8164098743634511)
f_1(x) = 0.25 * sin(4 * ω_y * (x - x(F)) + Δφ * π / 180) + y(F) - 0.65
f_2(x) = 0.25 * sin(4 * ω_x * (x - x(F))) + y(F)
g_1 = Function(f_1, x(F), x(F) + 2)
h_1 = Function(f_2, x(F), x(F) + 2)
I: F + (0, 0.3)
L: I + (2, 0)
M: F + (0, -0.95)
N: M + (2, 0)
mnohoúhelník1, m_1, n_1, l_1, i_1 = Polygon(M, N, L, I)