herclau

！...？！...

Answered: herclau 1043

September 29 2018

0 0

https://math.stackexchange.com/a/870326/520013

@Christopher2222 Yes, that's what I...

Answered: herclau 1043

September 29 2018

0 0

@Christopher2222

Yes, that's what I'm looking for the average of all the possible radios generated within the elliptical sector. with an uncertainty of 0.050 units of radius length

the average value of all these radios ge...

Answered: herclau 1043

September 29 2018

0 0

@Markiyan Hirnyk

When moving the segment on the left through the arch of the ellipse (red) to reach the segment on the right; the length (radius) of this varies. And I want to know the average value of all these radios generated in this tour

A solution for an approach to the method...

Answered: herclau 1043

February 01 2018

0 0

Thanks to the examples of one_man and the orientations of him !!!

restart; with(LinearAlgebra); with(plots); with(RootFinding)

R := 8:

(1)

x01 := 2.784;

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Matrix([[2*x1(s), 2*x2(s), -0.656e-3], [x2(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x2(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), x1(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x1(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), .2421035552]])

(11)

Matrix([[2*x1(s), 2*x2(s), -0.656e-3], [x2(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x2(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), x1(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x1(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), .2421035552]])

(12)

Vector[column]([[2*x1(s)*(diff(x1(s), s))+2*x2(s)*(diff(x2(s), s))-0.656e-3*(diff(v(s), s)) = 0], [(x2(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x2(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))))*(diff(x1(s), s))+(x1(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x1(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))))*(diff(x2(s), s))+.2421035552*(diff(v(s), s)) = 0]])

(13)

diff(x1(s), s) = 0.656e-3*x1(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+0.656e-3*sin(x1(s)*x2(s))*x1(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s)))+.4842071104*x2(s), diff(x2(s), s) = -.4842071104*x1(s)-0.656e-3*x2(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))-0.656e-3*sin(x1(s)*x2(s))*x2(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s)))

(14)

diff(v(s), s) = 2*x1(s)^2*sin(x1(s)*x2(s))*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s)))-2*x2(s)^2*sin(x1(s)*x2(s))*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s)))+2*x1(s)^2*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))-2*x2(s)^2*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))

(15)

(16)

(17)

(18)

(19)

(20)

$seq(printf("%20a x1= %6.14f x2= %6.14f f1:%3.3E f2:%3.3E \n", i, r1(i), r2(i), subs(x1 = r1(i), x2 = r2(i), f1), subs(x1 = r1(i), x2 = r2(i), f2)), i = 1 .. op(r1)[1])$

  1 x1= 2.54362646436683    x2= -1.23648695589547     f1:-1.064E-003   f2:1.536E-04
                   2 x1= 1.23548229113281    x2= -2.54421782426744     f1:-5.392E-004   f2:7.519E-05
                   3 x1= 0.00214159374757    x2= -2.82821913043411     f1:-1.172E-003   f2:-5.077E-03
                   4 x1= -0.40606484303441    x2= -2.79891801557864     f1:-1.169E-003   f2:2.324E-02
                   5 x1= -0.66911881748076    x2= -2.74793425583102     f1:-1.137E-003   f2:4.955E-03
                   6 x1= -0.82778070221595    x2= -2.70445143307415     f1:-7.216E-004   f2:3.431E-02
                   7 x1= -0.94907774854690    x2= -2.66424656651701     f1:-1.042E-003   f2:-1.767E-02
                   8 x1= -1.06040452186907    x2= -2.62190999920745     f1:-1.130E-003   f2:-1.427E-01
                   9 x1= -1.13985733604312    x2= -2.58837534455223     f1:-1.038E-003   f2:4.953E-02
                  10 x1= -1.21671835968973    x2= -2.55327279826836     f1:-3.945E-004   f2:-1.213E-02
                  11 x1= -1.31750650472367    x2= -2.50260203972384     f1:-1.160E-003   f2:-1.465E-01
                  12 x1= -1.39209309790707    x2= -2.46197354544288     f1:-7.631E-004   f2:1.644E-01
                  13 x1= -1.47479978375992    x2= -2.41334332694900     f1:-7.396E-004   f2:2.214E-01
                  14 x1= -1.53572710466028    x2= -2.37500967381226     f1:-8.713E-004   f2:-3.025E-01
                  15 x1= -1.59458156009475    x2= -2.33588416943076     f1:-9.548E-004   f2:3.202E-01
                  16 x1= -1.65374113659669    x2= -2.29436832079133     f1:-1.014E-003   f2:-2.720E-01
                  17 x1= -1.71376016165094    x2= -2.24984682776027     f1:-1.215E-003   f2:8.990E-02
                  18 x1= -1.78189858804577    x2= -2.19633920942737     f1:-9.315E-004   f2:1.276E-01
                  19 x1= -1.89236500479571    x2= -2.10193723163552     f1:-8.146E-004   f2:-1.231E-02
                  20 x1= -2.10182918210203    x2= -1.89266236584885     f1:-1.433E-004   f2:4.352E-03
                  21 x1= -2.19315791144590    x2= -1.78606355457922     f1:-3.535E-005   f2:7.009E-03
                  22 x1= -2.25482645476283    x2= -1.70719591347843     f1:-1.240E-003   f2:-1.020E-01
                  23 x1= -2.29874438889659    x2= -1.64762501165466     f1:-1.106E-003   f2:-9.721E-02
                  24 x1= -2.33839041537811    x2= -1.59083061731523     f1:-1.188E-003   f2:2.244E-01
                  25 x1= -2.37599441722105    x2= -1.53411813901912     f1:-1.132E-003   f2:-2.667E-01
                  26 x1= -2.41246421507361    x2= -1.47609086778904     f1:-1.172E-003   f2:2.437E-01
                  27 x1= -2.44829388649443    x2= -1.41588425018057     f1:-1.129E-003   f2:-1.825E-01
                  28 x1= -2.48390001965827    x2= -1.35246498616566     f1:-1.079E-003   f2:1.031E-01

                  29 x1= -2.52088197756227    x2= -1.28234712765565     f1:-7.399E-004   f2:-1.930E-02
                  30 x1= -2.55647418488492    x2= -1.21010104620827     f1:-9.520E-005   f2:-3.117E-03
                  31 x1= -2.55725103720352    x2= -1.20848742079778     f1:-2.529E-005   f2:2.636E-04
                  32 x1= -2.59199780479722    x2= -1.13167811871411     f1:-8.520E-004   f2:-1.238E-02
                  33 x1= -2.62403981264812    x2= -1.05511378686834     f1:-1.150E-003   f2:-8.282E-02
                  34 x1= -2.66477212249790    x2= -0.94787893078020     f1:-5.151E-004   f2:-3.720E-02
                  35 x1= -2.70328699154681    x2= -0.83178101747324     f1:-3.798E-004   f2:-3.827E-02
                  36 x1= -2.74830157756488    x2= -0.66761335699945     f1:-1.131E-003   f2:-1.862E-02
                  37 x1= -2.79892540273542    x2= -0.40627819459561     f1:-9.546E-004   f2:2.155E-02
                  38 x1= -2.82826491111433    x2= 0.00173681729463     f1:-9.146E-004   f2:-4.120E-03
                  39 x1= -2.54433101897068    x2= 1.23530962245658     f1:-3.898E-004   f2:6.229E-05
                  40 x1= -1.23671908966867    x2= 2.54349733417903     f1:-1.147E-003   f2:1.721E-04
                  41 x1= -0.00073458072575    x2= 2.82834704632849     f1:-4.524E-004   f2:-1.746E-03
                  42 x1= 0.40833537637737    x2= 2.79871881197279     f1:-4.352E-004   f2:5.465E-03
                  43 x1= 0.66841621959767    x2= 2.74828974489449     f1:-1.232E-004   f2:-5.306E-03
                  44 x1= 0.83195601028255    x2= 2.70309067653145     f1:-1.150E-003   f2:-4.054E-02
                  45 x1= 0.95704002378808    x2= 2.66138363143587     f1:-1.112E-003   f2:1.129E-01
                  46 x1= 1.04571314921648    x2= 2.62785867139441     f1:-8.428E-004   f2:3.707E-02
                  47 x1= 1.15532158077162    x2= 2.58148351131537     f1:-1.175E-003   f2:1.228E-01
                  48 x1= 1.25794637061984    x2= 2.53317036103230     f1:-6.189E-004   f2:3.598E-02
                  49 x1= 1.33165119737523    x2= 2.49511625497215     f1:-1.100E-003   f2:-9.277E-02
                  50 x1= 1.39488099797687    x2= 2.46032076956659     f1:-1.129E-003   f2:1.327E-01
                  51 x1= 1.45551306852179    x2= 2.42493286176428     f1:-1.182E-003   f2:-1.645E-01
                  52 x1= 1.51482650856934    x2= 2.38833924914073     f1:-1.136E-003   f2:1.949E-01
                  53 x1= 1.57360102215449    x2= 2.35001468708758     f1:-1.211E-003   f2:-2.414E-01
                  54 x1= 1.63317569347262    x2= 2.30902944303107     f1:-1.120E-003   f2:3.110E-01
                  55 x1= 1.70269135065952    x2= 2.25833533140894     f1:-7.637E-004   f2:-2.240E-01
                  56 x1= 1.78885426346953    x2= 2.19065178931709     f1:-1.045E-003   f2:-5.069E-02
                  57 x1= 1.89524505846999    x2= 2.09923097149235     f1:-1.275E-003   f2:2.435E-02
                  58 x1= 2.09944601281432    x2= 1.89500175505702     f1:-1.295E-003   f2:2.025E-02
                  59 x1= 2.19141698728636    x2= 1.78790969849667     f1:-1.070E-003   f2:-2.597E-02
                  60 x1= 2.25304165384425    x2= 1.70990394568866     f1:-3.180E-005   f2:-9.078E-03
                  61 x1= 2.31044040665652    x2= 1.63118118671915     f1:-1.113E-003   f2:3.582E-01
                  62 x1= 2.35201716381982    x2= 1.57060758708410     f1:-1.207E-003   f2:-3.098E-01
                  63 x1= 2.39046453994601    x2= 1.51146933790897     f1:-1.140E-003   f2:2.631E-01
                  64 x1= 2.42704556321628    x2= 1.45198796646780     f1:-1.181E-003   f2:-2.218E-01
                  65 x1= 2.46232322378804    x2= 1.39134233749253     f1:-1.131E-003   f2:1.730E-01
                  66 x1= 2.49703317598278    x2= 1.32805293458612     f1:-1.101E-003   f2:-1.144E-01
                  67 x1= 2.53584075572262    x2= 1.25258997230118     f1:-5.300E-004   f2:3.206E-02
                  68 x1= 2.58186667400809    x2= 1.15446924517573     f1:-1.165E-003   f2:1.206E-01
                  69 x1= 2.62805202051826    x2= 1.04529640142583     f1:-6.980E-004   f2:4.247E-02
                  70 x1= 2.66166589673867    x2= 0.95623086716168     f1:-1.157E-003   f2:1.000E-01
                  71 x1= 2.70333680782272    x2= 0.83114956898775     f1:-1.160E-003   f2:-2.603E-02
                  72 x1= 2.74805912501649    x2= 0.66929742702714     f1:-2.120E-004   f2:8.438E-03
                  73 x1= 2.79874307916961    x2= 0.40793702572444     f1:-6.246E-004   f2:8.611E-03
                  74 x1= 2.82831325375278    x2= -0.00106651234563     f1:-6.430E-004   f2:-2.533E-03
                  75 x1= 2.54348072644402    x2= -1.23674340424277     f1:-1.172E-003   f2:1.738E-04
                  76 x1= 1.23487145044661    x2= -2.54458645888873     f1:-1.723E-004   f2:2.783E-05

Download sistema9Dsarrollo.mw

update sistema9 from sistema9_1...

Answered: herclau 1043

January 31 2018

0 0

@one man

Thanks One_Man,
Thanks to your example with the file sistema9_1 I updated the file system9; I have obtained the expected result and even one of the graphics. All with the initial values for the systema {2.784, -0.5}.
In your sistema9_1 file with the initial values mentioned above, your procedure to find the roots returns the 82 expected points. But in the update do not work and the following error announces:
"Error, invalid input: rhs received sln (NextZero (proc (t) options operator, arrow; rhs (sln (t) [2]) end proc, 0, maxdistance = 14.985)) [3 .. 4], which is not valid for its 1st argument, expr "

R := 8:

(1)

(2)

(3)

Matrix([[2*x1(s), 2*x2(s), -0.656e-3], [x2(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x2(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), x1(s)*cos(x1(s)*x2(s))*sin(exp(x1(s)*x2(s)))+sin(x1(s)*x2(s))*x1(s)*exp(x1(s)*x2(s))*cos(exp(x1(s)*x2(s))), .2421035552]])

(4)

(5)

(6)

(7)

(8)

(9)

Error, invalid input: rhs received sln(NextZero(proc (t) options operator, arrow; rnops*hs(sln(t)[2]) end proc, 0, maxdistance = 14.985))[3 .. 4], which is not valid for its 1st argument, expr

Download sistema9.mw

How to obtain the next graphic :

Gracias

abs(1, x) or abs(x)?...

Answered: herclau 1043

December 06 2017

0 0

Independence of the function to take into account abs (1, x) or abs (x), the behavior of some of the critical points obtained is different. What is the correct choice?

>

solve([-(1.25*y-sqrt(abs(x)))*abs(1, x)/sqrt(abs(x))+2*x, 3.1250*y-2.50*sqrt(abs(x))], [x, y])

(1)

>	$solX := solve(((125(1/100))y-sqrt(abs(x)))^2+x^2-1 = 0, {y})$

${y = (4/5)*abs(x)^(1/2)+(4/5)*(-x^2+1)^(1/2)}, {y = (4/5)*abs(x)^(1/2)-(4/5)*(-x^2+1)^(1/2)}$

(2)

>

(3)

>

(4)

>

(5)

>

(6)

>

(7)

>

(8)

>

$with(plots); -1; p1 := pointplot([[evalf(c1)[1], point3], [evalf(c1)[2], point3], [0, point2], [0, point1]], color = [green], symbol = circle, axes = none, symbolsize = 15); -1; p2 := implicitplot(((125*(1/100))*y-sqrt(abs(x)))^2+x^2-1, x = -1 .. 1, y = -1 .. 1.3, axes = normal, gridrefine = 3); -1; display({p1, p2})$