Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

I want to arrange this equation in term of powers of x and then plot the  real and imagenery part of x vs y. How can I do this with Maple?
1-alpha*((1/x^2)+(1/(x-y)^2)+(1/(x+ay)^2))=0;

1.mw     (alpha and a are constant, for example alpha=1 and a=0.3)

I need help on maple code for solving both linear and non linear boudary condition for fractional order partial differential equation 

restart;
with(plots); with(LinearAlgebra);
_EnvHorizontalName := 'x';

_EnvVerticalName := 'y';

x1,y1,x2,y2,x3,y3:=0,-3,3,1,5,-2:   
A := [x1, y1]: B := [x2, y2]: C := [x3, y3]:

Barycentre := proc (A, B, t) description "Barycentre de 2 points A(1) et B(t) dans le rapport t";
return [(1-t)*A[1]+t*B[1], (1-t)*A[2]+t*B[2]] end proc;
ellip := proc (r1, r2) local a, b, c, d, e, f, D, E, F, eq1, eq2, eq3, eq4, eq5, eq6, x0, y0, EE, r3, sol, Ff, Tg;
global A, B, C;
r3 := -1/(r2*r1);
D := Barycentre(C, B, 1/(1-r1)); E := Barycentre(A, C, 1/(1-r2)); F := Barycentre(B, A, 1/(1-r3));
Ff := proc (x, y) options operator, arrow; a*x^2+2*b*x*y+c*y^2+2*d*x+2*e*y+f end proc;
Tg := proc (x0, y0, x, y) options operator, arrow; a*x*x0+b*(x*y0+y*x0)+c*y*y0+d*(x+x0)+e*(y+y0)+f end proc;
eq1 := Ff(D[1], D[2]);
eq2 := Ff(E[1], E[2]);
eq3 := Ff(F[1], F[2]);
eq4 := Tg(F[1], F[2], x1, y1);
eq5 := Tg(D[1], D[2], x2, y2);
eq6 := Tg(E[1], E[2], x3, y3);
sol := op(solve([eq1, eq2, eq3, eq4, eq5, eq6], [a, b, c, d, e]));
assign(sol);
EE := subs(f = 1, Ff(x, y) = 0) end proc;

ellip(-1, -7); tri := plot([A, B, C, A], color = blue):
 
po := plot([A, B, C], style = point, symbolsize = 15, symbol = solidcircle, color = red);
tp := textplot([[A[], "A"], [B[], "B"], [C[], "C"]], 'align' = {'above', 'left'});
x := 'x'; y := 'y';
ELL := seq(implicitplot(ellip(-7/11-(1/11)*j, -1/17-3*j*(1/17)), x = 0 .. 5, y = -3 .. 1, color = ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12])), j = 1 .. 17);
display([tri, ELL, po, tp], view = [-.5 .. 5.5, -4 .. 1.5], axes = none, scaling = constrained, size = [500, 500]);
Explore(implicitplot(ellip(r1, r2), x = 0 .. 5, y = -3 .. 1), parameters = [r1 = -2.18 .. -.7, r2 = -3 .. -.23]);
Can you tell me why this last instruction does't work ? Thank you.
 

We consider a triangle ABC, its circumscribed circle (O), of radius R, its inscribed circle (I) of centre I. We designate by α, β, γ the points of contact of BC, CA, AB with the circle (I), by A', B', C' the points of meeting other than A, B, C, of AI, BI, CI with the circle (O), by the media of BC, CA, AB.
.Establish that there is a conic (E), focus I, tangent to βγ, γα, αβ.
My code : 

restart;
with(geometry);
with(plots); _local(gamma);
_EnvHorizontalName := x; _EnvVerticalName := y;
alias(coor = coordinates);
point(A, -5, -5); point(B, 7, -1); point(C, 1, 5);
triangle(ABC, [A, B, C]); circumcircle(_O, ABC, 'centername' = OO); incircle(_I, ABC, 'centername' = Io);
line(lBC, [B, C]); sol := solve({Equation(_I), Equation(lBC)}, {x, y}); point(alpha, subs(sol, x), subs(sol, y));
line(lCA, [C, A]); sol := solve({Equation(_I), Equation(lCA)}, {x, y}); point(beta, subs(sol, x), subs(sol, y));
line(lAB, [A, B]); sol := solve({Equation(_I), Equation(lAB)}, {x, y}); point(gamma, subs(sol, x), subs(sol, y));
line(lAO, [A, OO]); intersection(Ap, lAO, lBC);
line(lBO, [B, OO]); intersection(Bp, lBO, lCA);
line(lCO, [C, OO]); intersection(Cp, lCO, lAB);
midpoint(l, B, C); midpoint(m, A, C); midpoint(n, A, B);
triangle(T, [alpha, beta, gamma]);
dr := draw([ABC(color = blue), _O(color = red), _I(color = magenta), lAO(color = black), lBO(color = black), lCO(color = black), T(color = red), alpha, beta, gamma, Ap, Bp, Cp, l, m, n], printtext = true);
display([dr], axes = normal, scaling = constrained, size = [800, 800]);
How to find the Equation of (E); Thank you.

We give a line (D) and a point A located at a distance AH=h from D. A constant angle of magnitude alpha pivots to its apex A and we call B and C the points where its sides cut the line D. Let O be the center of the circle circumscribed to the triangle ABC.
Demonstrate that the B and C tangents to the O circle keep a fixed direction. 
Here is my code which don't work for slopes are not equal.

restart; with(plots): with(geometry):unprotect(D):
_EnvHorizontalName := 'x':_EnvVerticalName := 'y':
line(D, y = (1/2)*x-1); point(A, 5, 5); PerpendicularLine(lp, A, D); h := distance(A, D); intersection(H, D, lp);
alpha := (1/16)*Pi;
rotation(lp1, lp, (1/6)*Pi, 'clockwise', A); rotation(lp2, lp1, (1/6)*Pi-alpha, 'clockwise', A); FindAngle(lp1, lp2); evalf(%);
intersection(B, D, lp1); intersection(C, D, lp2);
triangle(T, [A, B, C]);
circumcircle(Elc, T, 'centername' = OO);
TangentLine(tgB, B, Elc); TangentLine(tgC, C, Elc);
evalf(slope(tgB)); evalf(slope(tgC));
dr := draw([D(color = blue), lp(color = red), Elc(color = green), A, B, C, T(color = black), H, tgB, tgC], printtext = true);

display([dr], axes = none, scaling = constrained);
Fig := proc (k) local dr, Elc, B, C, lp1, lp2; global D, A, lp, H, alpha; geometry:-rotation(lp1, lp, (1/6)*Pi+k, 'clockwise', A); geometry:-rotation(lp2, lp1, (1/6)*Pi-alpha+k, 'clockwise', A); geometry:-intersection(B, D, lp1); geometry:-intersection(C, D, lp2); geometry:-triangle(T, [A, B, C]); geometry:-circumcircle(Elc, T, 'centername' = OO); geometry:-TangentLine(tgB, B, Elc); geometry:-TangentLine(tgC, C, Elc); dr := geometry:-draw([D(color = blue), lp(color = red), Elc(color = green), A, B, C, T(color = black), H, tgB, tgC], printtext = true); plots:-display([dr], axes = none, scaling = constrained) end proc;
iframes := 10;

display([seq(Fig((1/12)*Pi+i/(10*iframes)), i = 1 .. iframes)], insequence, scaling = constrained);
How to improve this code ? Thank you.

Eq=z"(t)+3z'(t)+2z(t)=24*(exp(-3t)-exp(-4t)) how to find the gereral solution of this equation. Thank you.

Hi, my problem is the next differential equation:

In maple. I used this code to solved it, but throws this error:

dsolve({diff(y(x), x, x) = -P*x/(I*E), eval(y(x), x = L) = 0, eval((D(y))(x), x = L) = 0});
Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(L), y(x)}

What is the problem with my code? How can solve my ODE with tis boundary conditions? 

 

 

What do I need to do to the "2 + 3" in the attached Document in order to make it evaluate? I know about F5 to switch between Text and Math modes, but that's not enough to get me where I want to be. The "2 + 3" is already in Math mode, but that's not enough to get it to evaluate.

The Document: t.mw

 

Download Analisa_Dinamik_Limb_v1_(30).mwAnalisa_Dinamik_Limb_v1_(30).mw

So I have an equation that basically takes the component of vectors to be used as an equation. The variables that I after are FB1z, FB2x, and FB3y For example here is my equation: 

EOM1:=(AFB1[1]+AFB2[1]+AFB3[1])=TEOM[1]

EOM2:=(AFB1[2]+AFB2[2]+AFB3[2])=TEOM[2]

EOM3:=(AFB1[3]+AFB2[3]+AFB3[3])-TEOM[3]:

FBBp1:=FBPP1=(EulP1[1]+EulP2[1]+EulP3[1]):
FBBp2:=FBPP2=(EulP1[2]+EulP2[2]+EulP3[2]):
FBBp3:=FBPP3=(EulP1[3]+EulP2[3]+EulP3[3]):

However there are unknown variable in AFB2[1] named FB2x and AFB3[1] named FB3y. Then AFB1[2] has unknown equation named FB1z and AFB3[2] has FB3y and so on. While in my FBBp1,FBBp2,and FBBp3 holds all of the variable of FB1z, FB2x, and FB3x
I have tried to use 'solve' command to find the variable but my computer won't stop processing it:
sls:=solve({EOM1,EOM2,EOM3,FBBp1,FBBp2,FBBp3},{FB1z,FB2x,FB3y}):

I tried to use the Gauss-Elimination by forming a matrix but it doesn't work as well since I am really confused how to take out the variables out of the vector component.

zzz:=Matrix([0,AFB2[1],AFB3[1],jjj[1]],[AFB1[2],0,AFB3[2],jjj[2]],[AFB1[3],AFB2[3],0,jjj[3]],[FBP1[1],FBP2[1],FBP3[1],EulP[1]],[FBP1[2],FBP2[2],FBP3[2],EulP[2]],[FBP1[3],FBP2[3],FBP3[3],EulP[3]]):
GaussElimination:=(zzz)

I would be very grateful If someone could help me. Thankyou

 

Edit: here are the .txt files and .mpl files that required to run the program 

Inverse_Kinematics_ADRIAN2.mw

RotInertiax0_ADRIAN.txt

Download DisplacementXYZ.txt

inersia_platfrom.txt

There is an .mpl file that I couldn't upload so I will upload it in the comments

 

How to draw a circle transfomed by orthogonal affinity to oblique line and k ration ? Thank you.

Etude d'un cas particulier a := 5: b := 7: k := 9: A := [a, 0]: B := [0, b]: #A et B fixes P := [t, 0]: Q := [0, k/t]:#P et Q 2 points mobiles cir := -a*x-b*y+x^2+y^2 = 0: sol := solve(subs(y = 5, cir), x): cen := [solve(diff(cir, x)), solve(diff(cir, y))]: x0 := sol[1]: y0 := 5: M := [x0, y0]: R := sqrt(cen[1]^2+cen[2]^2): beta := arctan(diff(solve(EQ(M, cen), y), x)): Recherche des valeurs de t pour que les 2 droites soient perpendiculaires eq := t^2*(y0-b)+t*(a*b-a*y0+b*x0-k)-x0*(a*b-k) = 0; sol := solve(eq, t); t := sol[1]; tp := sol[2]; P1 := [t, 0]; Q1 := [0, k/t]; PQ1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0:#1ere tangente PQ2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0:#2ième tangente P2 := [tp, 0]; Q2 := [0, k/tp]; CIR := implicitplot(cir, x = -4 .. 8, y = -4 .. 12, color = red); Fig := proc (alpha) local Dr1, DR1, Dr2, DR2, N, u0, v0, Po, t, tp, sol; global a, b, k, cen, R; u0 := cen[1]+R*cos(alpha); v0 := cen[2]+R*sin(alpha); N := [u0, v0]; sol := solve(t^2*(v0-b)+t*(b*u0-a*v0+a*b-k)-u0*(a*b-k) = 0, t); t := sol[1]; tp := sol[2]; Dr1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0; DR1 := implicitplot(Dr1, x = -4 .. 8, y = -4 .. 12, color = brown); Dr2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0; DR2 := implicitplot(Dr2, x = -4 .. 8, y = -4 .. 12, color = pink); Po := pointplot([N[]], symbol = solidcircle, color = [black], symbolsize = 8); display([Po, DR1, DR2]) end proc; DrPQ1 := implicitplot(PQ1, x = -4 .. 22, y = -4 .. 12, color = blue); DrPQ2 := implicitplot(PQ2, x = -4 .. 22, y = -4 .. 12, color = blue); Points := pointplot([A[], B[], M[], P1[], P2[], Q1[], Q2[], cen[]], symbol = solidcircle, color = [green], symbolsize = 10); T := plots:-textplot([[A[], "A"], [B[], "B"], [M[], "M"], [P1[], "P1"], [P2[], "P2"], [Q1[], "Q1"], [Q2[], "Q2"], [cen[], "cen"]], font = [times, 10], align = {below, left}); n := 19; display([seq(Fig(2*i*Pi/n), i = 0 .. n), Fig(beta), CIR, DrPQ1, DrPQ2, Points, T], scaling = constrained, size = [500, 500]); I would find out the focus of the ellipse. Thank you.

Hello

I use Maple 20018.2.

When I use "Data Set Search" and press Search I get following Error Message. I check that the network access to the internet is on enable. Does anybody has an Idea?

thank you

Murad

I'm trying to obtain the dynamical response of a simply-supported beam with a cantilever extension, coupled to a spring-mass system. In mathematical terms, this system is ruled by three PDEs (relative to each bare part of the main structure) and one ODE (relative to the spring-mass system). I think my mathemical model is finely formulated, but Maple keeps telling me this:

Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector

I believe it is because my PDEs depend on "x" and "t", while the ODE depends solely on "t". I have tried to transform my ODE into a "PDE", making it also dependent of "x", but without imposing any boundary conditions relative to "x". However, after this Maple points a new error message:

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

Could someone help me finding a solution? My algorythm in shown in the attached file below.

Worksheet.mw

Can anyone help me to frame the equations in Fractional Reduced Differential Transform Method 

system of nonlinear ordinary differential equations
ds/ dt = b−γ s(t)− (δ s(t)(i(t) + βa(t)) /N − ε s(t) m(t) 
de/ dt = δ (s(t)(i(t) + βa(t))/ N + ε s(t) m(t) − (1−ϑ) θ e(t) − ϑ α e(t) − γ e(t) 
di/ dt = (1−ϑ) θ e(t) − (ρ + γ) i(t)
da/ dt = ϑ α e(t) − (σ + γ) a(t)
dr /dt = ρ i(t) + σ a(t) − γ r(t)
dm /dt = τ i(t) + κ a(t) − ω m(t) 

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