Reibungskoeffizient ρ

rechts

unten

KM = (3.1492473371101544, 2.227837678418325)
ρ = 0.3 (slider from 0 to 0.5, step 0.01)
steigung = 0.37 (slider from 0 to 1, step 0.01)
α: atan(steigung)
E_0: (((2 * pi) * ρ) * cos(α))
F_k(x) = E_0 - ((x * ρ) * cos(α)) - ((1 - cos(x)) * sin(α))
O = Roots(F_k, 0, (2 * pi))
m: steigung / ρ
v_{normal}(x) = If[x ≤ (2 * pi), (F_k(0) - F_k(x)) / E_0]
F_k'(x) = F_k'(x)
P, A = Roots(F_k', 0, (2 * pi))
von: x(P)
v_{rutsch1}(x) = If[0 ≤ x ≤ von, (F_k(0) - F_k(x)) / E_0, 0]
Erutsch: F_k(x(P))
t(x) = Erutsch
V = Roots(F_k(x) - t(x), (3 * pi / 2), (2 * pi))
bis: x(V)
v_{rutsch3}(x) = If[bis < x ≤ (2 * pi), (F_k(0) - F_k(von)) / E_0 + (F_k(von) - F_k(x)) / E_0, 0]
v_{rutsch2}(x) = If[von < x ≤ bis, (F_k(0) - F_k(von)) / E_0, 0]
v_{stopp} = If(x(O) < (2 * pi), If[x < x(O), (F_k(0) - F_k(x)) / E_0, 1], (F_k(0) - F_k(x)) / E_0)
R_1 = Segment((0, 0), (0, E_0))
Startenergie = Point(R_1)
EkinStart: y(Startenergie)
E_k(x) = If[0 < x < (2 * pi), EkinStart - ((x * ρ) * cos(α)) - ((1 - cos(x)) * sin(α))]
N_1, N_2, N_3 = Roots(E_k, 0, (2 * pi))
reibungskoeffizient = 0.53 (slider from 0 to 1, step 0.00010)
f: x = (5 / 6 * pi)
g: x = (11 / 6 * pi)
f_1: x = pi / 6
f_2: x = pi / 2
f_4: x = (7 / 6 * pi)
f_5: x = (9 / 6 * pi)
i: x = (2 * pi)
Ursprung = Intersect(xAxis, yAxis)
G = Intersect(f_1, xAxis)
H = Intersect(f_2, xAxis)
I = Intersect(f, xAxis)
J = Intersect(f_4, xAxis)
K = Intersect(f_5, xAxis)
L = Intersect(g, xAxis)
M_1 = Intersect(i, xAxis)
R1: (x(KM) - sin(pi / 6), y(KM) - cos(pi / 6))
R2: (x(KM) - sin((3 * pi / 6)), y(KM) - cos((3 * pi / 6)))
R3: (x(KM) - sin((5 * pi / 6)), y(KM) - cos((5 * pi / 6)))
R4: (x(KM) - sin((7 * pi / 6)), y(KM) - cos((7 * pi / 6)))
R5: (x(KM) - sin((9 * pi / 6)), y(KM) - cos((9 * pi / 6)))
R6: (x(KM) - sin((11 * pi / 6)), y(KM) - cos((11 * pi / 6)))
j = Segment(R2, R5)
strecke = Segment(R4, R1)
l = Segment(R3, R6)
S: (x(KM) - sin(von), y(KM) - cos(von))
T: (x(KM) - sin(bis), y(KM) - cos(bis))
C = Intersect(E_k, xAxis, (2.039985328590482, 0))
Halt: {x(N_1), x(N_2), x(N_3)}
Z: (x(KM) - sin(x(N_1)), y(KM) - cos(x(N_1)))
E = Intersect(xAxis, yAxis)
A2: 1
A3: 2
A4 = 3
A5 = 4
A6 = 5
A7 = 6
A8 = 7
A9 = 8
A10 = 9
A11 = 10
A12 = 11
A13 = 12
A1: 0
B2: (((A2 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A2 * pi / 6))) * sin(α))
B3: (((A3 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A3 * pi / 6))) * sin(α))
B4: (((A4 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A4 * pi / 6))) * sin(α))
B5: (((A5 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A5 * pi / 6))) * sin(α))
B6: (((A6 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A6 * pi / 6))) * sin(α))
B7: (((A7 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A7 * pi / 6))) * sin(α))
B8: (((A8 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A8 * pi / 6))) * sin(α))
B9: (((A9 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A9 * pi / 6))) * sin(α))
B10: (((A10 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A10 * pi / 6))) * sin(α))
B11: (((A11 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A11 * pi / 6))) * sin(α))
B12: (((A12 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A12 * pi / 6))) * sin(α))
B13: (((A13 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A13 * pi / 6))) * sin(α))
B1: (((A1 * pi / 6) * ρ) * cos(α)) + ((1 - cos((A1 * pi / 6))) * sin(α))
F = Intersect(i, xAxis)
h = Segment(E, F)
M = Point(h)
b: (((2 * pi) * ρ) * cos(α))
MaximaleEnergie: (0, E_0)
verteilung(x) = If[0 ≤ x ≤ 6.283185307179586, If[m > 1, If[x(O) < (2 * pi), v_{stopp}, v_{rutsch1}(x) + v_{rutsch2}(x) + v_{rutsch3}(x)], v_{normal}]]
C1: verteilung(((A1 * 2) * pi / 12))
C2: verteilung(((A2 * 2) * pi / 12)) - verteilung(((A1 * 2) * pi / 12))
C3: verteilung(((A3 * 2) * pi / 12)) - verteilung(((A2 * 2) * pi / 12))
C4: verteilung(((A4 * 2) * pi / 12)) - verteilung(((A3 * 2) * pi / 12))
C5: verteilung(((A5 * 2) * pi / 12)) - verteilung(((A4 * 2) * pi / 12))
C6: verteilung(((A6 * 2) * pi / 12)) - verteilung(((A5 * 2) * pi / 12))
C7: verteilung(((A7 * 2) * pi / 12)) - verteilung(((A6 * 2) * pi / 12))
C8: verteilung(((A8 * 2) * pi / 12)) - verteilung(((A7 * 2) * pi / 12))
C9: verteilung(((A9 * 2) * pi / 12)) - verteilung(((A8 * 2) * pi / 12))
C10: verteilung(((A10 * 2) * pi / 12)) - verteilung(((A9 * 2) * pi / 12))
C11: verteilung(((A11 * 2) * pi / 12)) - verteilung(((A10 * 2) * pi / 12))
C12: verteilung(((A12 * 2) * pi / 12)) - verteilung(((A11 * 2) * pi / 12))
C13: verteilung(((A13 * 2) * pi / 12)) - verteilung(((A12 * 2) * pi / 12))
A19: 1
A20: 2
A21: 3
A22: 4
A23: 5
A24: 6
B19: C7 + C8
B20: C5 + C6
B21: C9 + C10
B22: C3 + C4
B23: C11 + C12
B24: C2 + C13
B25 = Sum(B19:B24)
B26 = Sum(C2:C7)
B27 = Sum(C8:C13)
RR: (x(KM), y(KM) - 1)
c = Circle(KM, 1)
d = CircleSector(KM, T, S)
R = If(x(O) < (2 * pi), (x(KM) - sin(x(O)), y(KM) - cos(x(O))))
e = CircleSector(KM, RR, R)
u = Vector(KM, Z)
D26: verteilung(pi)
D27: verteilung((2 * pi)) - verteilung(pi)
D28: verteilung((3 / 2 * pi)) - verteilung((1 / 2 * pi))
D29: 1 - D28
dichte(x) = If[0 ≤ x ≤ 6.283185307179586, verteilung'(x)]
A28: "p(oben)= " + ((D28 * 100)) + " %"
A26: "p(links) = " + ((D26 * 100)) + " %"
B232 = NaN
Text1: "" + B23 + ""
Text2: "" + B24 + ""
Text3: "" + B19 + ""
Text4: "" + B20 + ""
Text5: "" + B21 + ""
Text6: "" + B22 + ""
k: steigung / ρ
Text8: "k = steigung/ρ = " + k + ""