links

rechts

KM = (2.2808940561255566, 2.6310794288934782)
RR: (x(KM), y(KM) - 1)
reibungsfaktor = 0.3 (slider from 0 to 0.4, step 0.01)
steigung = 0.21 (slider from 0 to reibungsfaktor, step 0.01)
α: atan(steigung)
start(x) = ((x * reibungsfaktor) * cos(α)) + ((1 - cos(x)) * sin(α))
db(x) = If[0 ≤ x ≤ (2 * π), 1]
m: steigung / reibungsfaktor
E_0: (((2 * π) * reibungsfaktor) * cos(α))
F_k(x) = E_0 - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))
F_k'(x) = F_k'(x)
O = Roots(F_k, 0, (2 * π))
R_1 = Segment((0, 0), (0, E_0))
Startenergie = Point(R_1)
EkinStart: y(Startenergie)
E_k(x) = EkinStart - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))
N_1 = Roots(E_k, 0, (2 * π))
reibungskoeffizient = 0.53 (slider from 0 to 1, step 1.0E-4)
f: x = (5 / 6 * π)
g: x = (11 / 6 * π)
f_2(x) = ((start((3 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (3 * π / 6), 1])
f_4(x) = ((start((7 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (7 * π / 6), 1])
f_5(x) = ((start((9 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (9 * π / 6), 1])
i: x = (2 * π)
Ursprung = Intersect(xAxis, yAxis)
f_1(x) = ((start(π / 6) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ π / 6, 1])
G = Intersect(f_1, xAxis, (0.5235987775266755, -7.643210994667804E-10))
H = Intersect(f_2, xAxis, (1.5707963267948966, -5.551115123125783E-17))
I = Intersect(f, xAxis)
J = Intersect(f_4, xAxis, (3.6651914291880923, 1.1102230246251565E-16))
K = Intersect(f_5, xAxis, (4.71238898038469, -8.326672684688674E-17))
L = Intersect(g, xAxis)
R1: (x(KM) - sin(π / 6), y(KM) - cos(π / 6))
M_1 = Intersect(i, xAxis)
R2: (x(KM) - sin((3 * π / 6)), y(KM) - cos((3 * π / 6)))
R3: (x(KM) - sin((5 * π / 6)), y(KM) - cos((5 * π / 6)))
R4: (x(KM) - sin((7 * π / 6)), y(KM) - cos((7 * π / 6)))
R6: (x(KM) - sin((11 * π / 6)), y(KM) - cos((11 * π / 6)))
R5: (x(KM) - sin((9 * π / 6)), y(KM) - cos((9 * π / 6)))
j = Segment(R2, R5)
k = Segment(R4, R1)
l = Segment(R3, R6)
C = Intersect(E_k, xAxis, (2.2605807517796586, -4.503508677089485E-12))
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 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A2 * π / 6))) * sin(α))
B3: (((A3 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A3 * π / 6))) * sin(α))
B4: (((A4 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A4 * π / 6))) * sin(α))
B5: (((A5 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A5 * π / 6))) * sin(α))
B6: (((A6 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A6 * π / 6))) * sin(α))
B7: (((A7 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A7 * π / 6))) * sin(α))
B8: (((A8 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A8 * π / 6))) * sin(α))
B9: (((A9 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A9 * π / 6))) * sin(α))
B10: (((A10 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A10 * π / 6))) * sin(α))
B11: (((A11 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A11 * π / 6))) * sin(α))
B12: (((A12 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A12 * π / 6))) * sin(α))
B13: (((A13 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A13 * π / 6))) * sin(α))
B1: (((A1 * π / 6) * reibungsfaktor) * cos(α)) + ((1 - cos((A1 * π / 6))) * sin(α))
F = Intersect(i, xAxis)
h = Segment(E, F)
M = Point(h)
N: (0, start(x(M)))
b: (((2 * π) * reibungsfaktor) * cos(α))
MaximaleEnergie: (0, E_0)
verteilung(x) = If[0 ≤ x ≤ 6.283185307179586, (E_0 - ((0 * reibungsfaktor) * cos(α)) - (0 * sin(α)) - (E_0 - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α)))) / E_0]
C1: verteilung(((A1 * 2) * π / 12))
C2: verteilung(((A2 * 2) * π / 12)) - verteilung(((A1 * 2) * π / 12))
C3: verteilung(((A3 * 2) * π / 12)) - verteilung(((A2 * 2) * π / 12))
C4: verteilung(((A4 * 2) * π / 12)) - verteilung(((A3 * 2) * π / 12))
C5: verteilung(((A5 * 2) * π / 12)) - verteilung(((A4 * 2) * π / 12))
C6: verteilung(((A6 * 2) * π / 12)) - verteilung(((A5 * 2) * π / 12))
C7: verteilung(((A7 * 2) * π / 12)) - verteilung(((A6 * 2) * π / 12))
C8: verteilung(((A8 * 2) * π / 12)) - verteilung(((A7 * 2) * π / 12))
C9: verteilung(((A9 * 2) * π / 12)) - verteilung(((A8 * 2) * π / 12))
C10: verteilung(((A10 * 2) * π / 12)) - verteilung(((A9 * 2) * π / 12))
C11: verteilung(((A11 * 2) * π / 12)) - verteilung(((A10 * 2) * π / 12))
C12: verteilung(((A12 * 2) * π / 12)) - verteilung(((A11 * 2) * π / 12))
C13: verteilung(((A13 * 2) * π / 12)) - verteilung(((A12 * 2) * π / 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)
Text1: "" + B19 + ""
Text5: "" + B20 + ""
Text6: "" + B21 + ""
Text7: "" + B22 + ""
Text8: "" + B23 + ""
Text9: "" + B24 + ""
B26 = Sum(C2:C7)
B27 = Sum(C8:C13)
f_3(x) = ((start((5 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (5 * π / 6), 1])
f_6(x) = ((start((11 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (11 * π / 6), 1])
f_7(x) = ((start((12 * π / 6)) - ((x * reibungsfaktor) * cos(α)) - ((1 - cos(x)) * sin(α))) * If[0 ≤ x ≤ (12 * π / 6), 1])
n: x = π / 2
q: x = π / 6
r: x = (7 / 6 * π)
s: x = (9 / 6 * π)
s_4 = Segment((0, start(π / 6)), (0, start((3 * π / 6))))
s_2 = Segment((0, start((3 * π / 6))), (0, start((5 * π / 6))))
s_1 = Segment((0, start((5 * π / 6))), (0, start((7 * π / 6))))
sl_6 = Segment((0, start((0 * π / 6))), (0, start(π / 6)))
s6_6 = Segment((0, start((11 * π / 6))), (0, start((12 * π / 6))))
s_3 = Segment((0, start((7 * π / 6))), (0, start((9 * π / 6))))
s_5 = Segment((0, start((9 * π / 6))), (0, start((11 * π / 6))))
B: (0, start(π / 6))
W: (0, start((3 * π / 6)))
A_1 = Intersect(f_6, yAxis, (0, 1.718525937912954))
B_1 = Intersect(f_5, yAxis, (0, 1.5890560201870354))
C_1 = Intersect(f_4, yAxis, (0, 1.4595861024611165))
D_1 = Intersect(f_3, yAxis, (0, 1.1521330389276447))
E_1 = Intersect(f_1, yAxis, (0, 0.18126062024559692))
Text11: "rechts
 " + B27 + ""
Text10: "links
 " + B26 + ""
c = Circle(KM, 1)
u = Vector(KM, Z)
c_1 = CircleSector(KM, R4, R3)
d_1 = CircleSector(KM, R1, R6)
e_1 = CircleSector(KM, R6, R5)
g_1 = CircleSector(KM, R5, R4)
h_1 = CircleSector(KM, R3, R2)
k_1 = CircleSector(KM, R2, R1)
dichte(x) = verteilung'(x)
bergauf = Integral(dichte, π / 6, (5 * π / 6))
bergab = Integral(dichte, (7 * π / 6), (11 * π / 6))
berg = Integral(dichte, (5 * π / 6), (7 * π / 6))
Text4: "steigung/reibungsfaktor =" + m + ""