Lhunatic Exupery

## 15 Reputation

7 years, 188 days

## How tol solve a system of differential e...

Maple

Hi guys,

I'm trying to solve this system I have but the solution doesn't display:

-I have two second degree differential equations with two functions.

-I have a set of two boundary conditions per function.

Thank you!

 > restart;
 > eq2:=2*diff(y(x), x\$2)+diff(z(x), x\$2)=0;
 (1)
 > eq3:=2*diff(z(x), x\$2)+diff(y(x), x\$2)=0;
 (2)
 > SOL:=dsolve({eq2, eq3, D(y)(0)=0, D(y)(1)=1, D(z)(0)=0, D(z)(1)=1}, {y(x), z(x)});
 (3)

## How to solve a non linear first degree p...

Maple

Hello,

I have been trying to solve a simple nonlinear equation. Im interested in the solution per say rather than the plot but when I browsed about the commands to use, this came up. I tried it in my case and it is giving me the following errors:

 > restart;

 > with(plots);
 (1)
 > eq5:=C*sqrt(y(x)*((diff(y(x),x))^2+1))-y(x)=0;
 (2)
 > C:=1;
 (3)
 > bcs:=y(-1)=1, y(1)=1;
 (4)
 > dsys:={eq5,bcs};
 (5)
 > dsol:=dsolve(dsys, numeric); odeplot(dsol,[x,y(x)],0..1,color=red,axes=box);

## Extrapolation of a fourth degree tensor ...

Maple

Hey everyone!

My question is pretty straightforward: I have a second degree tensor and I need a fourth degree order one from it.

In Python, there is a command that performs the action, would there be one in Maple? Or any kind of process to go through to get the result?

Thanks

## Plots are not showing up...

Hello people,

Im trying to plot some expressions and Maple shows me an empty graph

Although the expressions are pretty weird, I have only one variable:

 > restart;
 > E[1]:=-3.27*10^(-10)*(-6.02*10^78-6.18*10^78*v)^2*(-9.23*10^232*v-1.15*10^232-9.03*10^232*v^3-1.74*10^233*v^2)*(-7.91*10^154-1.94*10^155*v-1.11*10^155*v^2)/(-4.31*10^534*v-3.11*10^535*v^4-3.13*10^535*v^3-3.90*10^533-3.28*10^534*v^6-1.59*10^535*v^5-1.66*10^535*v^2);
 (1)
 > plot(E[1], v=0..0.5);
 >

## How to obtain accurate rotation matrices...

Maple 2016

Hey guys,

I'm trying to build up some program to manage my composites data. But I am struggling with my compliance/stiffness in the global coordinates:

-Basically, I have the lamina's properties in local coordinates.

-When I make walls out of them with 30degress fibers orientation, I need to rotate the local stiffness several times to get the the stiffness of that particular wall.

-While I do understand the concept and manage to get the final rotation matrix correctly, I often find myself making mistakes regarding the sense of rotation of my local axis relatively to the global one.

I try to stick with one direction of rotation but if Maple has a smart way whereas I can plug in the initial configuration of the local coords relatively to the global one, show the final configuration (local aligned to the global), and get the rotation matrix that made it happen, it would be more helpful.

Thank you

Update:

I enclosed an example of the kind of operations I do:

And here is the kind of code I'm using:

 > restart:
 > with(LinearAlgebra):
 > Stiffness:=Matrix(6,6): Stiffness:=Matrix(6, 6, {(1, 1) = 20.4, (1, 2) = .537, (1, 3) = 1.01, (1, 4) = 0., (1, 5) = 0., (1, 6) = -0., (2, 1) = .537, (2, 2) = 1.59, (2, 3) = .73, (2, 4) = 0., (2, 5) = 0., (2, 6) = -0., (3, 1) = 1.01, (3, 2) = .73, (3, 3) = 2.86, (3, 4) = 0., (3, 5) = 0., (3, 6) = -0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 1.5, (4, 5) = 0., (4, 6) = -0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 2., (5, 6) = -0., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = .8});
 (1)
 > Q1:=Matrix(3,3): Q1[1,1]:=sin(Pi/4); Q1[1,2]:=0; Q1[1,3]:=cos(Pi/4); Q1[2,1]:=cos(Pi/4); Q1[2,2]:=0; Q1[2,3]:=-sin(Pi/4); Q1[3,1]:=0; Q1[3,2]:=1; Q1[3,3]:=0;
 (2)
 > Q1;
 (3)
 > Q2:=Matrix(3,3): Q2[1,1]:=0; Q2[1,2]:=0; Q2[1,3]:=1; Q2[2,1]:=1; Q2[2,2]:=0; Q2[2,3]:=0; Q2[3,1]:=0; Q2[3,2]:=1; Q2[3,3]:=0;
 (4)
 > Q2;
 (5)
 > Q3:=Matrix(3,3): Q3[1,1]:=0; Q3[1,2]:=-1; Q3[1,3]:=0; Q3[2,1]:=1; Q3[2,2]:=0; Q3[2,3]:=0; Q3[3,1]:=0; Q3[3,2]:=0; Q3[3,3]:=1;
 (6)
 > Q3;
 (7)
 > S1:=Transpose(Q1); S2:=Transpose(Q2); S3:=Transpose(Q3);
 (8)
 > S4:=Multiply(S3,S2);
 (9)
 > S5:=Multiply(S4,S1);
 (10)
 > R:=Matrix(6,6): R[1,1]:=S5[1,1]^2; R[1,2]:=S5[1,2]^2; R[1,3]:=S5[1,3]^2; R[2,1]:=S5[2,1]*S5[1,1]; R[2,2]:=S5[2,2]*S5[1,2]; R[2,3]:=S5[2,3]*S5[1,3]; R[3,1]:=S5[2,1]^2; R[3,2]:=S5[2,2]^2; R[3,3]:=S5[2,3]^2; R[1,4]:=2*S5[1,2]*S5[1,3]; R[1,5]:=2*S5[1,1]*S5[1,3]; R[1,6]:=2*S5[1,1]*S5[1,2]; R[2,4]:=S5[2,2]*S5[1,3]+S5[2,3]*S5[1,2]; R[2,5]:=S5[2,1]*S5[1,3]+S5[2,3]*S5[1,1]; R[2,6]:=S5[2,1]*S5[1,2]+S5[2,2]*S5[1,1]; R[3,4]:=2*S5[2,2]*S5[2,3]; R[3,5]:=2*S5[2,1]*S5[2,3]; R[3,6]:=2*S5[2,1]*S5[2,2];
 > R[4,1]:=S5[3,1]*S5[1,1]; R[4,2]:=S5[3,2]*S5[1,2]; R[4,3]:=S5[3,3]*S5[1,3]; R[4,4]:=S5[3,2]*S5[1,3]+S5[3,3]*S5[1,2]; R[4,5]:=S5[3,1]*S5[1,3]+S5[3,3]*S5[1,1]; R[4,6]:=S5[3,1]*S5[1,2]+S5[3,2]*S5[1,1]; R[5,1]:=S5[3,1]*S5[2,1]; R[5,2]:=S5[3,2]*S5[2,2]; R[5,3]:=S5[3,3]*S5[2,3]; R[5,4]:=S5[3,2]*S5[2,3]+S5[3,3]*S5[2,2]; R[5,5]:=S5[3,1]*S5[2,3]+S5[3,3]*S5[2,1]; R[5,6]:=S5[3,1]*S5[2,2]+S5[3,2]*S5[2,1];R[6,1]:=S5[3,1]^2; R[6,2]:=S5[3,2]^2; R[6,3]:=S5[3,3]^2; R[6,4]:=2*S5[3,3]*S5[3,2]; R[6,5]:=2*S5[3,1]*S5[3,3]; R[6,6]:=2*S5[3,1]*S5[3,2];
 (11)
 > print(R);
 (12)
 > RTrans:=Transpose(R);
 (13)
 > Stiff1:=Matrix(6,6): Stiff1:=Multiply(Stiffness, RTrans);
 (14)
 > StiffnessW1:=Matrix(6,6): StiffnessW1:=Multiply(R,Stiff1); evalf(StiffnessW1,3);
 (15)
 >

It is decent enough to get results if human mistakes don't happen when it comes to rotation orientation (which tends to happen more often than not).

I am aware though that it is not written with wits or in an efficient format. If you have a suggestion, Im all ears.

Thanks again

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