JAMET

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5 years, 117 days

MaplePrimes Activity


These are questions asked by JAMET

I try to eliminate m  in                    X := (a*m^2 + 2*m^2*p + 2*p)/(2*m^2)
                                                      Y := a/(2*m)

eliminate({X, Y}, m);
 allvalues(m);
without results. How can I do ? Thank you.

restart:with(LinearAlgebra):with(plots):with(geometry):with(plottools): On appelle alpha la moitié de l'angle de rotation de la roue menée par tour de roue menante. alpha=Pi/n en radians? soit Pi/8 pour 8 rainures.. On a alors les relations suivantes entre l'entaxe E, le rayon de la roue ùenante R1 et le rayon de la roue menée R2 : R1=E.sin(alpha), R2=E*cos(alpha) Intersection du cercle (O,R2) avec la droite tan(phi)x-r/cos(phi), on obtient les coordonnées de P3 sol:=allvalues(solve([tan(phi)*x-r/cos(phi)=y,y^2+x^2=R2^2],[x,y])): Intersection de 2 cercles sol1:=allvalues(solve([(x-E)^2+y^2=(R-a)^2,y^2+x^2=R2^2],[x,y])): Coordonnées des points du pourtour de l'élément de croix Oo:=point([0,0]): phi:=Pi/8:R2:=5:r:=1/4:E:=R2/cos(phi):evalf(%):R:=R2*tan(phi):evalf(%):a:=0.5: P1:=point([(R2/2-r)*cos(phi),(R2/2-r)*sin(phi)]): P2:=point([(R2/2)*cos(phi)+r*sin(phi),(R2/2)*sin(phi)-r*cos(phi)]): xP2:=(R2/2)*cos(phi)+r*sin(phi):yP2:=(R2/2)*sin(phi)-r*cos(phi): xP1:=(R2/2-r)*cos(phi):yP1:=(R2/2-r)*sin(phi): Equation paramétrique du segment OP1 (t varie de 0 à 1) ; x1:=t*(0-xP1)+xP1: y1:=t*(0-yP1)+yP1: n1:=5: dt:=1/(n1-1):#t varie entre 0 et 1 for i to n1 do tau:=(i-1)*dt: xx[i]:=evalf(subs(t=tau,x1)): yy[i]:=evalf(subs(t=tau,y1)): #print(i,xx[i],yy[i]); od: Equation paramétrique du quart de cercle P1P2 de la rainure (t varie de 0 à 1) x2:=R2/2*cos(phi)+r*cos(t):#attention au sens de rotation du parcours de l'objet y2:=R2/2*sin(phi)+r*sin(t): n2:=6: dt:=Pi/2/(n2-1):#arc de Pi/2 for i to n2 do tau:=phi-Pi+(i-1)*dt: xx[i]:=evalf(subs(t=tau,x2)): yy[i]:=evalf(subs(t=tau,y2)): od: for i to n2 do Vector[row]([i,xx[i],yy[i]]) od: droite:=plot((tan(phi)*x-r/cos(phi),x=0..3),linestyle=dot,color=blue): sol[1]: xP3:=evalf(subs(op(1,sol[1]),x)):yP3:=evalf(subs(op(1,sol[1]),y)): xP2:yP2: xP4:=evalf(subs(op(1,sol1[1]),x)):yP4:=evalf(subs(op(1,sol1[1]),y)): xP5:=E-(R-a):yP5:=0: x3:=t*(xP3-xP2)+xP2: y3:=t*(yP3-yP2)+yP2: n3:=10: dt:=1/(n3-1):#t varie entre 0 et 1 for i to n3 do tau:=(i-1)*dt: xx[i+n2]:=evalf(subs(t=tau,x3)): yy[i+n2]:=evalf(subs(t=tau,y3)): od: for i to n3 do Vector[row]([i,xx[i],yy[i]]) od: x4:=xP5+R-a+(R-a)*cos(t):#attention au sens de rotation du parcours de l'objet y4:=(R-a)*sin(t): n4:=11: eta:=arcsin(yP4/(R-a)): dt:=(-eta)/(n2-1)/2:#arc de Pi/2 for i to n4 do tau:=(Pi+eta)+(i-1)*dt:#recherche de tau ? xx[i+n2+n3]:=evalf(subs(t=-tau,x4)): yy[i+n2+n3]:=evalf(subs(t=-tau,y4)): od: for i to n4 do Vector[row]([i,xx[i],yy[i]]) od: n:=n2+n3+n4; n := 27 for i to n do Vector[row]([i,xx[i],yy[i]]) od: figure:=NULL: for i from 0 to n do xx[0]:=0:yy[0]:=0: figure:=figure,[xx[i],yy[i]]: #print(i,xx[i],yy[i]); od: polygonplot([figure],scaling=constrained,color=yellow,view=[-0.1..5,-0.1..3]): for i to n do X[i]:=xx[i]: Y[i]:=yy[i] od: d1:=plottools[disk]([xP1,yP1],0.05,color=blue): d2:=plottools[disk]([xP2,yP2],0.05,color=red): d3:=plottools[disk]([xP3,yP3],0.05,color=green): d4:=plottools[disk]([xP4,yP4],0.05,color=green): d5:=plottools[disk]([xP5,yP5],0.05,color=green): fig:=pointplot([figure],scaling=constrained): Po:=pointplot([[xP1,yP1],[xP2,yP2],[xP3,yP3]],color = blue, symbol = asterisk): Cir:=plot([R2*cos(t),R2*sin(t),t=0..Pi/2],color=black): Arc:=plot([E+(R-a)*cos(t),(R-a)*sin(t),t=3*Pi/4..Pi],linestyle=dot,color=blue): textplot({[1, 2, "one point in 2-D"], [3, 2, "second point in 2-D"]}): texte:=textplot([[xP1-0.2,yP1,"P1"],[xP2,yP2-0.3,"P2"],[xP3+0.2,yP3+0.2,"P3"], [xP4+0.2,yP4+0.1,"P4"],[xP5-0.2,yP5+0.2,"P5"]]): display({Arc,Cir,d1,d2,d3,d4,d5,Po,fig,droite,texte},scaling=constrained,view=[-1..7,-1..6]): with(plottools): printlevel:=3: Miroir : symétrie par rapport à l'axes des x for i from 0 to n/2 do tt:=yy[i]: yy[i]:=yy[n-i+1]: yy[n-i+1]:=tt: tt:=xx[i]: xx[i]:=xx[n-i+1]: xx[n-i+1]:=tt od: for i from 0 to n-1 do xx[2*n-i]:=xx[i]: yy[2*n-i]:=-yy[i]: #print(i,xx[i],yy[i]) od: Poly:=NULL: for i from 0 to 2*n-1 do xx[0]:=0:yy[0]:=0: Poly:=Poly,[xx[i],yy[i]]:od: polygonplot([Poly],color=yellow,scaling=constrained): pointplot([Poly],color = blue, scaling=constrained,symbol = asterisk,view=[-1..5,-3..3]): Rotation unassign('xt','yt'): #gc(): zt:=8:#8 rainures ou faisceaux xt:=Vector(63,[]): yt:=Vector(63,[]): xt:=Vector((2*n-1),zt,[]): yt:=Vector((2*n-1),zt,[]): j:=0: for k from 0 to zt-1 do j:=0: phi:=2*Pi*k/zt: cs:=cos(phi): sn:=sin(phi): for kk from 1 to 2*n-1 do j:=j+1: xt[j][k]:=evalf(xx[kk]*cs-yy[kk]*sn): yt[j][k]:=evalf(xx[kk]*sn+yy[kk]*cs): od: od: N1:=j: points:=seq(seq([xt[i][j], yt[i][j]], j=0..zt-1), i=1..2*n-1): p_cross:= pointplot([points], scaling = constrained, color = black,linestyle=solid, filled=[yellow]): polygonplot([points], color = yellow, scaling = constrained); NULL; display([p_cross]);#How to draw this cross with a line without points. Thank you.
I am trying to anime a pump but itn't working. I need help. Thank you. restart; with(plots); with(plottools); unprotect(D); alpha := arctan(-58/62.5); solve({k*Pi/100 = alpha}, {k}); beta := arctan(19/84); solve({k*Pi/100 = beta}, {k}); ang1 := arctan(-68/84); evalf(solve({k = ang1}, {k})); ang2 := arctan(55/84); evalf(solve({k = ang2}, {k})); #angular head travel Head := proc(k) local r, poly, k1, tC, tD, tE, DikC, DikD, DikE; global C, D, E; r := 84; C := [-55, 17]; D := [0, 0]; E := [84, 0]; poly := [[-60, 24], [63, -17], [60, -55.5], seq([r*cos(1/100*k*Pi), r*sin(1/100*k*Pi)], k1 = -24 .. 7), [82, 18], [78, 20], [64, -3], [-46.5, 35]]; tC := textplot([C[], "C"], align = {above, right}, font = [Times, bold, 18]); tD := textplot([D[], "D"], align = {above, left}, font = [Times, bold, 18]); tE := textplot([E[], "E"], align = {above, left}, font = [Times, bold, 18]); DikC := disk(C, 1, color = black); DikD := disk(D, 1, color = black); DikE := disk(E, 1, color = black); if 0

Would you tel me why this code doesn't work : the  lenghts of BC and BD are not constant. Thank you very much.
restart;
with(plots);
with(plottools);
AB := 39;
BC := 140;
BD := 140;
local(D);
Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc;
dist := proc(M, N) sqrt(Vdot(expand(M - N), expand(M - N))); end proc;
Fig := proc(alpha)
local cir, R, BC, BD, AC, AD, lAC, A, lBC, lAB, lBD, beta, B, C, Cc, Dd, D, Aa, Bb, F1, F2, d, k, h, i, Pb, Ph, pb1, ph1, Qb, Qh, qh1, qb1, p1, P1, p2, P2, p3, P3, p4, P4, q1, Q1, q2, Q2, q3, Q3, q4, Q4, cy1, cy2, cy3, cy4, tA, tB, tC, tD;
A := [0, 0]; R := 39; d := 83; BC := 140; BD := 140;
B := [R*cos(alpha), R*sin(alpha)];
k := BC/R; h := 1/2*sqrt(2);
Ph := [h*(R + BC), h*(R + BC)];
Pb := [h*(-R + BC), h*(-R + BC)];
Qh := [-h*(R + BC), h*(R + BC)];
Qb := [-h*(-R + BC), h*(-R + BC)];
P1 := [Ph[1] - 1/2*d*h, Ph[2] + 1/2*d*h];
P2 := [Ph[1] + 1/2*d*h, Ph[2] - 1/2*d*h];
P3 := [Pb[1] - 1/2*d*h, Pb[2] + 1/2*d*h];
P4 := [Pb[1] + 1/2*d*h, Pb[2] - 1/2*d*h];
Q1 := [Qh[1] + 1/2*d*h, Qh[2] + 1/2*d*h];
Q2 := [Qh[1] - 1/2*d*h, Qh[2] - 1/2*d*h];
Q3 := [Qb[1] + 1/2*d*h, Qb[2] + 1/2*d*h];
Q4 := [Qb[1] - 1/2*d*h, Qb[2] - 1/2*d*h];
cir := circle(A, R, color = black, linestyle = longdash);
F1 := plot(x, x = -R .. R + BC, color = black, linestyle = longdash);
F2 := plot(-x, x = -R - BC .. R, color = black, linestyle = longdash);
AC := R*(cos(alpha) + sqrt(k^2 - sin(alpha)^2));
C := [h . AC, h . AC];
AD := R*(cos(Pi - alpha) + sqrt(k^2 - sin(Pi - alpha)^2));
D := [-h*AD, h*AD]; lBC := plot([B, C], color = red, thickness = 4);
lAB := plot([A, B], color = red, thickness = 4); print(evalf(dist(B, C)), evalf(dist(B, D)));
lBD := plot([B, D], color = red, thickness = 4);
pb1 := pointplot(Pb, symbol = solidcircle, symbolsize = 5, color = black);
ph1 := pointplot(Ph, symbol = solidcircle, symbolsize = 5, color = black);
qb1 := pointplot(Qb, symbol = solidcircle, symbolsize = 5, color = black);
qh1 := pointplot(Qh, symbol = solidcircle, symbolsize = 5, color = black);
p1 := pointplot(P1, symbol = solidcircle, symbolsize = 10, color = black);
p2 := pointplot(P2, symbol = solidcircle, symbolsize = 10, color = black);
p3 := pointplot(P3, symbol = solidcircle, symbolsize = 10, color = black);
p4 := pointplot(P4, symbol = solidcircle, symbolsize = 10, color = black);
q1 := pointplot(Q1, symbol = solidcircle, symbolsize = 10, color = black);
q2 := pointplot(Q2, symbol = solidcircle, symbolsize = 10, color = black);
q3 := pointplot(Q3, symbol = solidcircle, symbolsize = 10, color = black);
q4 := pointplot(Q4, symbol = solidcircle, symbolsize = 10, color = black);
Aa := pointplot(A, symbol = solidcircle, symbolsize = 12, color = blue);
Bb := pointplot(B, symbol = solidcircle, symbolsize = 12, color = blue);
Cc := pointplot(C, symbol = solidcircle, symbolsize = 12, color = blue);
Dd := pointplot(D, symbol = solidcircle, symbolsize = 12, color = blue);
cy1 := plot([P1, P3], color = black, thickness = 8); cy2 := plot([P2, P4], color = black, thickness = 8);
cy3 := plot([Q1, Q3], color = black, thickness = 8); cy4 := plot([Q2, Q4], color = black, thickness = 8);
tA := textplot([0, 0, "A"], 'align' = {'above', 'right'});
tB := textplot([B[1], B[2], "B"], 'align' = {'above', 'right'});
tC := textplot([C[1], C[2], "C"], 'align' = {'above', 'right'});
tD := textplot([D[1], D[2], "D"], 'align' = {'above', 'right'});
display([cir, F1, F2, pb1, ph1, qb1, qh1, p1, p2, p3, p4, q1, q2, q3, q4, Aa, Bb, Cc, Dd, lAB, lBC, lBD, cy1, cy2, cy3, cy4, tA, tB, tC, tD], scaling = constrained); end proc;
Fig(Pi/3);
display([seq(Fig((2*alpha*Pi)/50), alpha = 0 .. 50)], insequence = true, axes = none);

Justify that 2 vectors (1,1) and (1,2) are an R² base; How to write calculations correctly ?
<x, y> = lambda*<1, 1> + mu*<1, 2>:
 solve({lambda+mu=x,lambda+2*mu=y},{lambda,mu}):
 <x, y> := (2*x - y)*<1, 1> + (-x + y)*<1, 2>:
Thank you.

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