Maple 2016 Questions and Posts

Shade Area/Region Between Polar Curve...

Asked by: huddy_99 10

March 15 2020

2 2

with(plots);
P1 := plot([-sin(t), t, t = 0 .. 2*Pi], coords = polar, color = red);
P2 := plot([cos(t), t, t = 0 .. 2*Pi], coords = polar, color = blue);
display(P1, P2, scaling = constrained);

I have two polar equation in the same graph but how do i shade the region between those two polar curve?

What could have happened to solve command?...

Asked by: Awe gbemisola 10

February 28 2020

2 2

Good day house.

Please I don't know why the solve command does not display any results in the following code. Kindly assist. Thank you in anticipation.

restart;
omega := v/h;
t := sum(a[j]*x^j, j = 0 .. 6)+a[7]*cos(omega*x)+a[8]*sin(omega*x);
r1 := diff(t, x$2);
r2 := diff(t, x$4);
c1 := eval(t, x = q+2*h) = y[n+2];
c2 := eval(r1, x = q) = f[n];
c3 := eval(r1, x = q+h) = f[n+1];
c4 := eval(r1, x = q+2*h) = f[n+2];
c5 := eval(r1, x = q+3*h) = f[n+3];
c6 := eval(r2, x = q) = g[n];
c7 := eval(r2, x = q+h) = g[n+1];
c8 := eval(r2, x = q+2*h) = g[n+2];
c9 := eval(r2, x = q+3*h) = g[n+3];
b1 := seq(a[i], i = 0 .. 8);
`k&Assign;solve`({c1, c2, c3, c4, c5, c6, c7, c8, c9}, {a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]});

Can someone help with the simplification of this c...

Asked by: abdulganiy 145

February 28 2020

0 0

Please I found out that the MatrixInverse on the assignment statement P3 does not run for about three days now. Please kindly help to simplify the code. Thank you and kind regards.

restart; omega := v/h;
r := a[0]+a[1]*x+a[2]*sinh(omega*x)+a[3]*cosh(omega*x)+a[4]*cos(omega*x)+a[5]*sin(omega*x);
b := diff(r, x);

c := eval(b, x = q) = f[n];
d := eval(r, x = q+3*h) = y[n+3]; e := eval(b, x = q+3*h) = f[n+3];
g := eval(b, x = q+2*h) = f[n+2];
i := eval(b, x = q+h) = f[n+1];
j := eval(b, x = q+4*h) = f[n+4];
k := solve({c, d, e, g, i, j}, {a[0], a[1], a[2], a[3], a[4], a[5]});
Warning,  computation interrupted
assign(k);
cf := r;
s4 := y[n+4] = simplify(eval(cf, x = q+4*h));
s3 := y[n+2] = simplify(eval(cf, x = q+2*h));
s2 := y[n+1] = simplify(eval(cf, x = q+h));
s1 := y[n] = simplify(eval(cf, x = q));

with(LinearAlgebra);
with(plots);
h := 1;
YN_1 := seq(y[n+k], k = 1 .. 4);
A1, a0 := GenerateMatrix([s1, s2, s3, s4], [YN_1]);
eval(A1);
YN := seq(y[n-k], k = 3 .. 0, -1);
A0, b1 := GenerateMatrix([s1, s2, s3, s4], [YN]);
eval(A0);
FN_1 := seq(f[n+k], k = 1 .. 4);
B1, b2 := GenerateMatrix([s1, s2, s3, s4], [FN_1]);
eval(B1);
FN := seq(f[n-k], k = 3 .. 0, -1);
B0, b3 := GenerateMatrix([s1, s2, s3, s4], [FN]);
eval(B0);
ScalarMultiply(R, A1)-A0;
det := Determinant(ScalarMultiply(R, A1)-A0);
P1 := A1-ScalarMultiply(B1, z);
P2 := combine(simplify(P1, size), trig);
P3 := MatrixInverse(P2);
P4 := A0-ScalarMultiply(B0, z);
P5 := MatrixMatrixMultiply(P3, P4);
P6 := Eigenvalues(P5);
f := P6[4];
T := unapply(f, z);
implicitplot(f, z = -5 .. 5, v = -5 .. 5, filled = true, grid = [5, 5], gridrefine = 8, labels = [z, v], coloring = [blue, white]);

How to get the real and imaginary parts of complex...

Asked by: Alger 524

February 20 2020

0 3

Hi all,

How to get the real and imaginary parts of this complex expression.

Thank you in advance

real_imag_parts.mw

How do I sort a formula in the following form...

Asked by: ing123 5

February 20 2020

1 0

Hello,

I want to sort the formulae to Psi and Beta, but I don't know how it works. I have tried it with sort, simplify, isolate, but that isn't what I'm searching.

It should looks like the simplier formula in the picture.

ab := (diff(Psii(t), t, t))*J-l[f]*(F[s, f, l]+F[s, f, r])+l[r]*(F[s, r, l]+F[s, r, r])-(1/2)*b[r]*(-F[s, r, l]*delta[l]+F[s, r, r]*delta[r]) = 0;
/ d / d \\
|--- |--- Psii(t)|| J - l[f] (F[s, f, l] + F[s, f, r])
\ dt \ dt //

+ l[r] (F[s, r, l] + F[s, r, r])

1
- - b[r] (-F[s, r, l] delta[l] + F[s, r, r] delta[r]) = 0
2
bc := (diff(betaa(t), t, t))*m*v*betaa(t)+F[s, r, l]*delta[l]+F[s, r, r]*delta[r]-(diff(Psii(t), t)) = 0;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t) + F[s, r, l] delta[l]
\ dt \ dt //

/ d \
+ F[s, r, r] delta[r] - |--- Psii(t)| = 0
\ dt /
cd := (diff(betaa(t), t))*m*v+F[s, r, l]+F[s, r, r]+F[s, f, l]+F[s, f, r]-(diff(Psii(t), t)) = 0;
/ d \
|--- betaa(t)| m v + F[s, r, l] + F[s, r, r] + F[s, f, l]
\ dt /

/ d \
+ F[s, f, r] - |--- Psii(t)| = 0
\ dt /
F[s, f, l] := c[fl]*alpha[fl];
c[fl] alpha[fl]
F[s, f, r] := c[fr]*alpha[fr];
c[fr] alpha[fr]
F[s, r, l] := c[rl]*alpha[rl];
c[rl] alpha[rl]
F[s, r, r] := c[rr]*alpha[rr];
c[rr] alpha[rr]
alpha[fl] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(-v+(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /
alpha[fr] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(v-(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
v - - b[f] |--- Psii(t)|
2 \ dt /
alpha[rl] := delta[l]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v+(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[l] + -----------------------------
1 / d \
-v + - b[r] |--- Psii(t)|
2 \ dt /
alpha[rr] := delta[r]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v-(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[r] + -----------------------------
1 / d \
-v - - b[r] |--- Psii(t)|
2 \ dt /

ab;
/
|
/ d / d \\ |
|--- |--- Psii(t)|| J - l[f] |
\ dt \ dt // |
|
\

/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
-------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /

/ / d \\\ / /
c[fr] |-v betaa - l[f] |--- Psii(t)||| | |
\ \ dt //| | |
+ -------------------------------------| + l[r] |c[rl] |delta[
1 / d \ | | |
v - - b[f] |--- Psii(t)| | | |
2 \ dt / / \ \

/ d \\
-v betaa + l[r] |--- Psii(t)||
\ dt /|
l] + -----------------------------|
1 / d \ |
-v + - b[r] |--- Psii(t)| |
2 \ dt / /

/ / d \\\ /
| -v betaa + l[r] |--- Psii(t)||| |
| \ dt /|| 1 |
+ c[rr] |delta[r] + -----------------------------|| - - b[r] |
| 1 / d \ || 2 |
| -v - - b[r] |--- Psii(t)| || |
\ 2 \ dt / // \
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
-c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\ \
| -v betaa + l[r] |--- Psii(t)|| |
| \ dt /| |
+ c[rr] |delta[r] + -----------------------------| delta[r]| =
| 1 / d \ | |
| -v - - b[r] |--- Psii(t)| | |
\ 2 \ dt / / /

0
bc;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t)
\ dt \ dt //

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------| delta[r]
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ d \
- |--- Psii(t)| = 0
\ dt /
cd;
/ d \
|--- betaa(t)| m v
\ dt /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------|
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------|
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
+ -------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /

/ / d \\
c[fr] |-v betaa - l[f] |--- Psii(t)||
\ \ dt // / d \
+ ------------------------------------- - |--- Psii(t)| = 0
1 / d \ \ dt /
v - - b[f] |--- Psii(t)|
2 \ dt /

How can the center of this sphere be determined?...

Asked by: Earl 955

February 09 2020

1 4

The sphere with radius 0.5 whose center has y coordinate = 0.5 and z coordinate = 0.5 is tangent internally to the ellipsoid centered on the origin with principal semi axes of 5, 3 and 2.

How can the x coordinate of the sphere's center be determined?

How would a springy brachistochrone behave?...

Asked by: Earl 955

January 23 2020

0 2

Imagine a brachistochrone shaped path made of a frictionless flexible metal strip which reacts to the force of a weighty sliding object.

Depending on its flexibility and the object's mass, what would be the strip's initial shape for fastest descent between its top and bottom? How would its shape change during the object's descent?

Perhaps an aircraft emergency escape slide or the fastest path for a slalom skier exemplify this kind of situation.

Histogram with the bars adjacent to each other?...

Asked by: Agha 40

January 16 2020

1 10

How can I draw a "regular looking" histogram where all the bars adjacent to each other?

I tried looking into the options for histograms with no luck. I included a picture of what kind of output I am looking for.

Thanks in advance.

ImageTools Permission Denied Error...

Asked by: Adam Ledger 360

January 15 2020

0 4

I am just confused to be getting this error seeings FileTools does not encounter this error when I use it's ListDirectory command:

error_for_primes.mw

>

(1)

>	$Read("H:\\MAPLE\\Image_Project", format = JPEG)$

Error, (in readbytes) permission denied

>

Download error_for_primes.mw

Number of Partitions of a number...

Asked by: Adam Ledger 360

January 13 2020

0 6

I couldnt find this command in the number theory package, as far as what i am thinking of doing it should be straight forward but very long winded, so if I have missed this command throughout the packages up to Maple 2016 I would appreciate someone telling me otherwise I suppose it's what i am doing for the next few hours

https://en.wikipedia.org/wiki/Partition_(number_theory)

What is the equation of motion of a swinging, hang...

Asked by: Earl 955

December 30 2019

3 6

A flexible rope of constant linear density hangs from one fixed end.

The lower end is pulled aside and then released.

The rope swings back and forth with a whip-like action.

What equation of motion can be used to animate this action in Maple?

I cannot find any references through Google to the appropriate math.

What logic is used to constructed an implicit plot...

Asked by: Earl 955

December 30 2019

0 7

Please explain the logic used to construct the plot below.

plots:-implicitplot(r >= cos(theta), r = 0 .. 1/3, theta = 0 .. 2*Pi, filledregions, coords = polar, numpoints = 5000, scaling = constrained)

How can I code the eventfired option in a numeric ...

Asked by: Earl 955

December 14 2019

2 2

The help page for dsolve,numeric,events says that "A call to a procedure-form dsolve numeric procedure" can return the time that one or more events fired by coding the eventfire option.

I do not know how to code for this.

Please provide a simple example of a procedure-form dsolve numeric with an event that exhibits this feature.

problem with solving N coupled differential equati...

Asked by: samkh 5

December 12 2019

1 1

Hello,

I want to write a code about numerical solving N(for example N=150) coupled differential equations (ODE ) with M boundary conditions in Maple but I do not know how to do it and I cannot find anything useful. in particular, I have trouble inserting boundary conditions which are a lot for N coupled difrential equations.

Does somebody have a code script on this matter? please let me know.

Thanks a bounch in advance.

How can Hooke's law be modified for a spring const...

Asked by: Earl 955

December 04 2019

2 6

For a spring hanging vertically from a fixed point, suppose the spring constant, k, is a function of the distance from the fixed point to the other (lowest) end of the spring (for example; the diameter of the spring's coils changes along the length of the spring) .

What ODE reflecting this situation will yield solutions for the harmonic motion of the spring after it is stretched from its equilibrium position?

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