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.
The system of equations x*y*z + y*z + y = 21, x*y*z + x*z + z = 30, x*y*z + x*y + x = 12
has three solutions, one of them is not an integer solution.
solve({x*y*z + y*z + y = 21, x*y*z + x*z + z = 30, x*y*z + x*y + x = 12}, {x, y, z})
How can I find three numbers a, b, c so that the system of equations
x*y*z + y*z + y = a, x*y*z + x*z + z = b, x*y*z + x*y + x = c
has three solutions (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), where x1, y1, z1, x2, y2, z2, x3, y3, z3 are nine integer numbers.
Hi,
Happy New Years All
Can anyone explain two document formating features I am trying to implement?
1.) Sections. I select numbering with follow previous selected and I get three sections with a 1. in front of them vs 1, 2, 3.
I would expect Technical to become 3.1 when properly following Section 3. header. Also, I have seen how to manually type the section number, but that seems to defeat the document layout and formatting if it gets "jumbled up".
2.) Headers. Can you suppress headers on pages 2 through X to have a unique cover page header? This would be similar to word (headers and footers linked to previous section, or not(?) with section breaks as new pages)
Thanks,
Bill
I am translating old Maple code to run on Maple 2021.2. This code from 1985. I think it was Maple 3 then. I'll put a link to the paper and page number.
It uses this syntax
Btw, the " above is meant to be % in new Maple. I do not know what w='@W' is supposed to translate to.
The paper is
A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS
by Carolyn J. Smith.
Here is the link
https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf
The above is at page 67. Near the end. The code also uses some old functions, which are not given in the listing, I searched but could not find these.. One is called Lsolve (to solve linear equations, but I can replace this with solve) and on page 77 it uses these
Functions required: scanmap, expcontract, lncontract, explnsimp
These are not given in the source code in the paper. I assume these are old Maple function which no longer exist?. But I can just use simplify for now in their place.
My question is on the use of `@W` and what it could mean? This syntax @ is used in many places in this old Maple code.
