https://drive.google.com/file/d/0B2D69u2pweEvU3NpWWQwS3U1XzQ/edit?usp=sharing
https://drive.google.com/file/d/0B2D69u2pweEvMnFabkdiX1hpYVk/edit?usp=sharing

a1 := Diff(x1(s,t),s$2) = a*x1(s,t)+b*x2(s,t)+c*x3(s,t)+d*u(t);
a2 := Diff(x1(s,t),t)=x1(s,t);
b1 := Diff(x2(s,t),s$2) = e*x1(s,t)+f*x2(s,t)+g*x3(s,t)+h*u(t);
b2 := Diff(x2(s,t),t)=x2(s,t);
c1 := Diff(x3(s,t),s$2) = i*x1(s,t)+j*x2(s,t)+k*x3(s,t)+l*u(t);
c2 := Diff(x3(s,t),t)=x3(s,t);
sys := [a1, a2, b1, b2, c1, c2];
sol := pdsolve(sys);

length exceed limit

Hi,

I get the error in the following code

restart:

gama1:=0.01:

zet:=0;
#phi0:=0.00789:
Phiavg:=0.02;
lambda:=0.01;
Ha:=1;


                               0
                              0.02
                              0.01
                               1
rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])*(1-Ha^2*u(eta))+((1/(eta)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta));
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(-2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)+k(eta)/k1[w]/(eta)*diff(T(eta),eta) ));
eq3:=diff(phi(eta),eta)+phi(eta)/(N[bt]*(1+gama1*T(eta))^2)*diff(T(eta),eta);
      /  d   /  d         \\   mu1[w] (1 - u(eta))
      |----- |----- u(eta)|| + -------------------
      \ deta \ deta       //         mu(eta)      

           /             /  d           \\               
           |      mu_phi |----- phi(eta)||               
           | 1           \ deta         /| /  d         \
         + |--- + -----------------------| |----- u(eta)|
           \eta           mu(eta)        / \ deta       /
                                /      /                        
                                |      |                        
/  d   /  d         \\     1    |      |  rho(eta) c(eta) u(eta)
|----- |----- T(eta)|| + ------ |k1[w] |- ----------------------
\ deta \ deta       //   k(eta) |      |         5000 p2        
                                \      \                        

                                /  d           \
     (a[k1] + 2 b[k1] phi(eta)) |----- phi(eta)|
                                \ deta         /
   + -------------------------------------------
                                          2     
         1 + a[k1] phi1[w] + b[k1] phi1[w]      

            /  d         \\\
     k(eta) |----- T(eta)|||
            \ deta       /||
   + ---------------------||
           k1[w] eta      ||
                          //
                                      /  d         \
                             phi(eta) |----- T(eta)|
          /  d           \            \ deta       /
          |----- phi(eta)| + ------------------------
          \ deta         /                          2
                             N[bt] (1 + 0.01 T(eta))
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,eq1):
eq2:=subs(phi(0)=phi0,eq2):
eq3:=subs(phi(0)=phi0,eq3):

#A somewhat speedier version uses the fact that you really need only compute 2 integrals not 3, since one of the integrals can be written as a linear combination of the other 2:
Q:=proc(pp2,fi0) local res,F0,F1,F2,a,INT0,INT10,B;
global Q1,Q2;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve(subs(p2=pp2,phi0=fi0,{eq1=0,eq2=0,eq3=0,u(1)=lambda/(phi(1)*rhop/rhobf+(1-phi(1)))*D(u)(1),D(u)(0)=0,phi(1)=phi0,T(1)=0,D(T)(1)=1}), numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
INT0:=evalf(Int((1-eta)*F0(eta),eta=0..1-zet));
INT10:=evalf(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet));
B:=(-cbf*rhobf+cp*rhop)*INT10+ rhobf*cbf*INT0;
a[1]:=2/(1-zet^2)*B-10000*pp2;
a[2]:=INT10/INT0-Phiavg;
Q1(_passed):=a[1];
Q2(_passed):=a[2];
if type(procname,indexed) then a[op(procname)] else a[1],a[2] end if
end proc;
#The result agrees very well with the fsolve result.
#Now I did use a better initial point. But if I start with the same as in fsolve I get the same result in just about 2 minutes, i.e. more than 20 times as fast as fsolve:

Q1:=proc(pp2,fi0) Q[1](_passed) end proc;
Q2:=proc(pp2,fi0) Q[2](_passed) end proc;
Optimization:-LSSolve([Q1,Q2],initialpoint=[6.5,exp(-1/N[bt])]);


proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
              HFloat(6.5), HFloat(0.006737946999)

the error is :

Error, (in Optimization:-LSSolve) system is singular at left endpoint, use midpoint method instead

how can I fix it.

Thanks

Amir

I have exported Maple code as a Maplet file.  When I click on the file Maplet Launcher opens but nothing "runs".  It looks like it's trying because the icon flashes, but no window opens.  The Maple worksheet from which the Maplet was generated runs fine.

Any suggestions as to how to get Maplet Launcher to run my Maplets?

Thanks,

Rollie

Hello,

In a mechanical problem, i have to deal with a system with trigonometric expression. The variables are gamma[1](t), psi[1](t), phi[1](t), alpha(t), beta(t), x(t). The orthers are parameters.

I would like to have a explicit relations between  gamma[1](t), psi[1](t), phi[1](t) and alpha(t), beta(t), x(t).

In orthers words, i would like to have 

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Of course, the expresions of alpha(t), beta(t), and x(t) should be complex. Nevertheless, it will avoid me to have to solve Newton Raphson algorithm to solve these constraints equations.

Normally, it should be feasible.

When i have only one equation and not a system, isolate function is helpful.

But in this case, i don't manage to have my relations.

Have you some ideas to expression these relations ?

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Here the code of the equations :

restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
eq_liai[1]:= rF[1]*cos(a[1])-cos(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*cos(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*cos(a[1])*sin(gamma[1](t))*sin(psi[1](t))-sin(a[1])*sin(phi[1](t)))-cos(alpha(t))*rBTP[1]*cos(a[1])-sin(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-sin(alpha(t))*cos(beta(t))*h = 0;
eq_liai[2]:= rF[1]*sin(a[1])-sin(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*sin(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*sin(a[1])*sin(gamma[1](t))*sin(psi[1](t))+cos(a[1])*sin(phi[1](t)))-cos(beta(t))*rBTP[1]*sin(a[1])+sin(beta(t))*h = 0;
eq_liai[3] := h[1]+sin(gamma[1](t))*e[1]+l[1]*(sin(gamma[1](t))*cos(psi[1](t))+cos(gamma[1](t))*sin(psi[1](t)))*cos(phi[1](t))+sin(alpha(t))*rBTP[1]*cos(a[1])-cos(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-cos(alpha(t))*cos(beta(t))*h-z(t) = 0;

or directly a maple file

constraints.mw

Thanks a lot for your help

Hi,

Does Maplesim allow hardware integration such as a joystick so that I can feed in joystick commands (via USB or serial) from the computer and then control my Maplesim model in the virtual space? Suggestions?

Thank you.

Hi,

I'm currently working on a manipulator model in Maplesim and will import CAD attachments to each of the links. The Solidworks model, once imported to Maplesim, is not located in the same position as the Maplesim part but is offset by X,Y,Z. The scaling is also off. Is there some way to align the CAD to the component instead of trial and error?

Thank you.

Maple Player seems like it could be an outstanding piece of software, yet with the new operating system for Ipad, the program crashes immediately. I am unable to find any solutions. I also stumbled across a post in which Maplesoft is no longer providing support for the APP. Is this true?

@Markiyan Hirnyk 

First try, i change to 

result1 := Optimization:-Minimize([ans>=0, ans<=0],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

Error, (in Optimization:-Minimize) objective function must be an algebraic expression or procedure

Second try, i change to use ans for >=0, ans2 <=0

ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2>=0,i=1..N)
end proc;
ans2:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2<=0,i=1..N)
end proc;
ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003);
result1 := Optimization:-Minimize([ans, ans2],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

Error, (in Optimization:-Minimize) objective function must be an algebraic expression or procedure

x11 := [0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]:
y11 := [ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]:
z11 := [ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]: 
u11 := [7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7];
a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);
b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);
c1 := Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t)+k12*u1(t);
d1 := Diff(u1(t),t) = 0;
ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1],u1(1)=u11[1];
sol:=dsolve({a1,b1,c1,d1, a2,b2,c2,d2,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12],output=listprocedure);
X,Y,Z,U:=op(subs(sol,[x1(t),y1(t),z1(t),u1(t)]));
tim := [seq(n, n=1..27)];
N:=nops(tim):
ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2,i=1..N)
end proc;
ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003);
result1 := Optimization:-Minimize([ans>=0, ans<=0],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

In my research a I need to solve the linear equation (getting its null space) under some constraints.

The matrix is given below:

The constraints shall be (x[1]...x[16]>0, x[17]...x[20] arbitary...)

The solutions shall actually be a canonical combination of a lot of vectors, (canonical combination means possitive sums of vectors). And I wish to get those vectors. is there a way that I could achieve this by Maple?

When you use the slider without Do(%MathContainer1 = StandardError(Variance, R)):
everything works ok but when you add Do(%MathContainer1 = StandardError(Variance, R)):
Maple Crashes.....

Strange...

LL_102)_Covariance_M.mw

@Markiyan Hirnyk 

First try, i change to 

result1 := Optimization:-Minimize([ans>=0, ans<=0],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

Error, (in Optimization:-Minimize) objective function must be an algebraic expression or procedure

Second try, i change to use ans for >=0, ans2 <=0

ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2>=0,i=1..N)
end proc;
ans2:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2<=0,i=1..N)
end proc;
ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003);
result1 := Optimization:-Minimize([ans, ans2],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

Error, (in Optimization:-Minimize) objective function must be an algebraic expression or procedure

x11 := [0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]:
y11 := [ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]:
z11 := [ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]:
u11 := [7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7];
a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);
b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);
c1 := Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t)+k12*u1(t);
d1 := Diff(u1(t),t) = 0;
ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1],u1(1)=u11[1];
sol:=dsolve({a1,b1,c1,d1, a2,b2,c2,d2,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12],output=listprocedure);
X,Y,Z,U:=op(subs(sol,[x1(t),y1(t),z1(t),u1(t)]));
tim := [seq(n, n=1..27)];
N:=nops(tim):
ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2,i=1..N)
end proc;
ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003);
result1 := Optimization:-Minimize([ans>=0, ans<=0],initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

hi,

     there is a common  differential equation in my maple note,the solution of the eq. can be expressed by

associated Legendre function(s),but i get a result by hypergeometric representation.how i can translate the later into a  single Legendre fun？

 Thank you in advance  

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Is there a way to play animations in maplets?

I can send an animation to a plotter, but don't know how to play it.  

Thanks, Rollie

I have a linear space spanned by the column vectors of:

I want to know its exact intersection of the first quadrant in 16 dimensional space (meaning Sum(a[i]*e[i]),i=1..16), how could I accomplish it? The output could possibly be the vectors defining the convex cone in higher dimensional space...