Hi everyone

I am trying to get the maximum value (angle) for a function, which is a solution from a ODE. I tried evalf(max.. which I already thaught wouldnt work. 

After that I installed the package "DirectSearch", again with no success. 

Does anybody know what I am doing wrong or how I am going to get the maximum. I added the maple file with the direct seach attempt. 

Thank you in advance!

Hi

I'd like to know that why in the attachment "fsolve" does not work?

How can I evaluate the value of "A" in my file?

Many thanks in advance

Download A.mw

Hi everyone 

I would like to plot something in 3d. I have to functions both depending on the time. (x(t), z(t))

I can plot in 2d: (t, x(t)) or (t,z(t)) or (x(t), z(t)) 

Now I want to show the flight path (x(t), z(t)) over time t. So I thought a 3d plot would be suitable for this. 

The problem is that I dont know how to plot this. With plot3d I am only able to plot some planes. What I want to plot is the flight path in the 3d room with the axis x(t),z(t) and t.

Does anybody know how to do this?

thanks in advance!

L’éventail de la Geisha
restart:with(plots):with(geometry):
NULL;
_EnvHorizontalName := 'x':
_EnvVerticalName := 'y':

NULL;
EqBIS := proc(P, U, V) 
local a, eq1, M1, t, PU, PV, bissec1; 
description "P est le sommet de l'angle dont on chercche la bissectrice" ;
a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2); 
M1 := P + a*t; eq1 := op(eliminate({x = M1[1], y = M1[2]}, t)); 
RETURN(op(eq1[2])); end proc:

with(plottools);
with(plots);

r1 := 1/2;
r2 := r1/2;
R := r1*(21 - 12*sqrt(3));
                            21      (1/2)
                       R := -- - 6 3     
                            2            

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);
b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);

with(geometry);
eq := EqBIS(<sqrt(3)/2, 1/2>, <0, 0>, <0, 1/2>);
line(bis, eq);
                         (1/2)                  
                eq := 2 3      y - 2 x + 4 y - 2

                              bis

OpT := 2*sqrt(r1*R);
line(lv, x = OpT);
intersection(Omega, bis, lv);
coordinates(Omega);
evalf(%);
                                (1/2)    
                      OpT := 2 3      - 3

                               lv

                             Omega

                 [                / (1/2)    \]
                 [   (1/2)      2 \3      - 1/]
                 [2 3      - 3, --------------]
                 [                     (1/2)  ]
                 [                2 + 3       ]

                  [0.464101616, 0.3923048456]

retarrt;
with(plots);
with(plottools);
[cos((5*Pi)/6), sin((5*Pi)/6)];
                        [  1  (1/2)  1]
                        [- - 3     , -]
                        [  2         2]

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);
b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);
NULL;
A:=[cos(Pi/6), sin(Pi/6)];
B:=[cos(5*Pi/6), sin(5*Pi/6)];
Oo:=[0,0];
Op:=[0,1/2];
poly:=[A,B,Oo];
R := r1*(21 - 12*sqrt(3))
                            [1  (1/2)  1]
                       A := [- 3     , -]
                            [2         2]

                           [  1  (1/2)  1]
                      B := [- - 3     , -]
                           [  2         2]

                          Oo := [0, 0]

                                [   1]
                          Op := [0, -]
                                [   2]

                [[1  (1/2)  1]  [  1  (1/2)  1]        ]
        poly := [[- 3     , -], [- - 3     , -], [0, 0]]
                [[2         2]  [  2         2]        ]

                            21      (1/2)
                       R := -- - 6 3     
                            2            

Omega := [2*sqrt(3) - 3, 2*(sqrt(3) - 1)/(2 + sqrt(3))];
Omega1 := [3 - 2*sqrt(3), 2*(sqrt(3) - 1)/(2 + sqrt(3))];

                     [                / (1/2)    \]
                     [   (1/2)      2 \3      - 1/]
            Omega := [2 3      - 3, --------------]
                     [                     (1/2)  ]
                     [                2 + 3       ]

                     [                 / (1/2)    \]
                     [    (1/2)      2 \3      - 1/]
           Omega1 := [-2 3      + 3, --------------]
                     [                      (1/2)  ]
                     [                 2 + 3       ]

r3 := 3/16;
EF := sqrt(r3);

                                  3 
                            r3 := --
                                  16

                               1  (1/2)
                         EF := - 3     
                               4       

r := (150 - 72*sqrt(3))/193*1/2;
alpha := -5/3*r + 1/2*1/2;
p := sqrt(3)/3*1/2 - sqrt(3)/18*r;
                          75    36   (1/2)
                     r := --- - --- 3     
                          193   193       

                             307   60   (1/2)
                  alpha := - --- + --- 3     
                             772   193       

               1  (1/2)   1   (1/2) /75    36   (1/2)\
          p := - 3      - -- 3      |--- - --- 3     |
               6          18        \193   193       /

p2 := textplot([[A[], "A"], [B[], "B"], [Oo[], "O"]], align = ["above", "right"]);
display(a, b, p2, polygonplot(poly, thickness = 3, color = blue, transparency = 0.3), circle(Omega, R, color = blue, filled = true), circle(Omega1, R, color = blue, filled = true), circle([0, 3/4], 1/4, color = yellow, filled = true), circle([EF, 1/2 + r3], r3, color = green, filled = true), circle([-EF, 1/2 + r3], r3, color = green, thickness = 5), circle([p, 3/4 + alpha], r, color = red, thickness = 5), circle([-p, 3/4 + alpha], r, color = red, thickness = 5), axes = none, scaling = constrained, size = [500, 500]);
how to put color inside circles ? Thabk you.

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 11:
r := 7:
a := sqrt(R*r):

b := 2:
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [R + 2*b + r, 0]), r]):
ellipse(p, (x - R - b)^2/b^2 + y^2/a^2 = 1):
draw([C1(color = yellow, filled = true), 
C2(color = red, filled = true), p(color = blue, filled = true), 
C1(color = black), C2(color = black), p(color = black)], 
axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained):
alpha := arctan((R - r)/(R + 2*b + r));
long := cos(alpha)*(R + 2*b + r);
evalf(%);
circle(C2, [point(P2, [long, r - R]), r]);
rotation(p1, p, alpha, 'clockwise');
detail(p1);
point(A, 0, -R);
point(B, long, -R);
line(L1, [A, B]);
point(cen, [(143*sqrt(5))/25, -(26*sqrt(5))/25]);
reflection(L2, L1, cen);
detail(L2);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  L2

draw([C1(color = yellow, filled = true), C2(color = red, filled = true), p1(color = blue, filled = true), C1(color = black), C2(color = black), p1(color = black), L1(color = black)], axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained);
A Bug in reflection ? Why these error messages. Thank you.

I wonder if there is any way to use ArrayInterpolation with contourplot or similar effect?

N_data.xlsx 

Thank you in advance,

Download test1.mw

I do not know what is the problem with Using ImportMatrix. N_data.xlsx is in the same directory.

Any comment would be appreciated.

Download test1.mw

polysols(diff(u(x), x) = u(x)^2 - 1) produces no results, while it can be verified by direct observation that u(x) = 1 is a polynomial solution.

I can not spawn draw the circles C3 and C4

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 7:
point(A, [0, R]):
line(L1, y = sqrt(3)*x + R):
line(L2, y = -sqrt(3)*x + R):
line(L3, y = R/3):
intersection(B, L1, L3):
intersection(C, L2, L3):
detail(C):
triangle(ABC, [A, B, C]):
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [0, R/3 + (2*R)/9]), (2*R)/9]):
detail(C2):
center(C2), coordinates(center(C2)):
reflection(P3, P2, C):
detail(P3):
reflection(C3, C2, C);
detail(C3):
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C3
circle(C3, [point(P3*[(28*sqrt(3))/9, 7/9]), (2*R)/9]):
Error, (in geometry:-point) wrong number of arguments
reflection(C4, C2, B);
detail(C4);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C4
circle(C3*[point(P3, [(28*sqrt(3))/9, 7/9]), (2*R)/9]);
Error, (in geometry:-circle) wrong number of arguments

draw([L1(color = blue), 
ABC(color = red, transparency = 0.5, filled = true), 
L2(color = blue), L3(color = blue), 
C1(color = blue, thickness = 3), C1(color = yellow, transparency = 0.8, filled = true), C2(color = blue, filled = true)], 
axes = normal,
 view = [-R .. R, -R .. R], 
scaling = constrained);
Why these error messages. Thank you veru much.

fig([L1(color = blue), L2(color = blue), L3(color = green), C1(color = black), C2(color = black), C3(color = orange), C4(color = orange)]);
point(oo, [0, 0]);
                               oo

rotation(fig1, fig, oo, Pi/2, 'counterclockwise');
Error, (in geometry:-rotation) wrong type of arguments why thos error ? Thank you;
 

What should I do to reduce evaluating time?

Download Negativity_v1.mw

I have the function: f(x)= sqrt(x) for x>=0; f(x)=1/x for x<0 and I would like to plot the function.

How exactly to implement this?

restart;
with(plots): with(geometry):
_EnvHorizontalName := 'x':
_EnvVerticalName := 'y':
a := 7:
point(E, 0, a*sqrt(3)/2):
point(B, -a/2, 0):
point(C, a/2, 0):
point(o, 0, a*sqrt(3)/6):
point(A, 0, a/2):
point(H, 0, 0):
R := (3-sqrt(3))*sqrt(2)*a/12:
point(J, 0, a*sqrt(3)/6 - R):
triangle(Tr1, [E, B, C]):
triangle(Tr2, [A, B, C]):
StretchRotation(E1, E, B, Pi/4, clockwise, sqrt(2)/2);
coordinates(E1);
StretchRotation(E2, E, C, Pi/4, counterclockwise, sqrt(2)/2);
coordinates(E2);
triangle(Tr3, [E, B, E1]);
triangle(Tr4, [E, C, E2]);
triangle(Tr5, [B, C, J]);
circle(cir, [point(P1,[0,a*sqrt(3)/6]), R]):
poly := Matrix([[0, a*sqrt(3)/2], [-7/4 + (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4], [0, a/2], [7/4 - (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4]], datatype = float);
pol1 := polygonplot(poly, colour = "Magenta", transparency = 0.7, gridlines);
tex := textplot([0.2, a*sqrt(3)/2, "zE"], 'align' = {'above', 'right'});
draw([Tr1(color = cyan),
Tr3(color = green),
tex,
cir(color=blue),
Tr2(color = red),
Tr4(color = grey),
Tr1(color=blue)],'view' = [-5 .. 5, 0 .. 7], 
axes = normal, scaling = constrained,size=[800,800]);
Error, (in geometry:-draw) the option must be of type equation or name
line(L1, [B, o]);
Equation(L1);
line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0);
reflection(J1, J, L1);
triangle(Tr6, [B, J1, E]);
line(L2, [C, o]);
Equation(L2);
line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0);
reflection(J3, J, L2);
triangle(Tr7, [C, J3, E]);
triangle(T1, [E, J1, A]);
triangle(T2, [E, C, E2]);
triangle(T3, [B, H, J]);
triangle(T4, [C, H, J]);

draw([cir(color = orange, filled = true, transparency = 0.1), pol1, Tr6(color = blue, filled = true, transparency = 0.2), Tr5(color = blue, filled = true, transparency = 0.2), Tr7(color = blue, filled = true, transparency = 0.2), T1(color = green, filled = true, transparency = 0.2), T2(color = green, filled = true, transparency = 0.2), T3(color = green, filled = true, transparency = 0.2), T4(color = green, filled = true, transparency = 0.2)], axes = none, scaling = constrained);
Error, (in geometry:-draw) the option must be of type equation or name
NULL;
NULL;

Why these errors messages ? Thank you.

Download U.m.mw

Hello im an amateur using maple for my hidraulics machines course at engineering school. Does anyone know how to use the degrees package on maple 2021, i called it out by using the short form. with(Degrees): and then try to use sind but it doesnt recognice the command.

Also when using RPMs the units that should be giving me m/s appear as m²/m*s(radious). I know that the software recognice it as angular speed but is there anyway to eliminate the (radious) so i can work with the speed as lineal?