## Plotting eigenvectors...

I'm trying to plot the lines that are based on eigenvectors of the matrix. (Functions r1(t),r2(t), q(t) are defined earlier. I can upload file if necessary)

with(LinearAlgebra):
x1:=t->-r1(t)*cos(Pi/2-q(t)/2):
y1:=t->-r1(t)*sin(Pi/2-q(t)/2):
z1:=t->0:
x2:=t->r2(t)*cos(Pi/2-q(t)/2):
y2:=t->-r2(t)*sin(Pi/2-q(t)/2):
z2:=t->0:
Ixx:=t->m*(y1(t)^2+z1(t)^2)+m*(y2(t)^2+z2(t)^2):
Iyy:=t->m*(x1(t)^2+z1(t)^2)+m*(x2(t)^2+z2(t)^2):
Izz:=t->m*(x1(t)^2+y1(t)^2)+m*(x2(t)^2+y2(t)^2):
Ixy:=t->-m*x1(t)*y1(t)-m*x2(t)*y2(t):
Ixz:=t->-m*x1(t)*z1(t)-m*x2(t)*z2(t):
Iyz:=t->-m*y1(t)*z1(t)-m*y2(t)*z2(t):

InertiaTensor:=t-><<Ixx(t),Ixy(t),Ixz(t)>|<Ixy(t),Iyy(t),Iyz(t)>|<Ixz(t),Iyz(t),Izz(t)>>:

Here I define the matrix as a function of time.

EV:=t->Eigenvectors(InertiaTensor(t));
V1:=t->Column(Re(EV(t)[2]),1);
V2:=t->Column(Re(EV(t)[2]),2);

Producing two eigenvectors also as functions of time.

InertiaAxis1 := t->plot(x, V1(t)[2]*x/V1(t)[1], x = -2 .. 2);
InertiaAxis2 := t->plot(x, V2(t)[2]*x/V2(t)[1], x = -2 .. 2);

InertiaAxis1(1);

And here I've got an error:

Error, (in plot) unexpected options: [-HFloat(7.378655652881484e-6)*x, x = -2 .. 2]

I tried to set "datatype=float"-option in plot function, to evaluate the coefficient by eval-function, it wouldn't help. What does this error mean exactly?

## How to compute the convex hull of points with both...

I would like compute the vertices of the convex hull of finitely many points in some \mathbb{R}^{n}, where the coordinates of these points could be rational numbers or irrational numbers like \sqrt{2}.

I know that PolyhedralSets[ConvexHull] is a direct command, however it does not support irrational numbers. But if I transform all coordinates into floating point numbers, for some rational numbers the rounding error would be large enough to affect the result. For example, after the transform some collinear points are no longer collinear.

Thanks!

## How to show numerical results (float) using engine...

When doing numerical calculations or evaluations it is very useful to have float results shown in numeric notation, where the exponent is 3 * n.

Below are some simple calculations:

Is there a way to make Maple show the resultin (1) .. (3) as:

• 333.3 106
• 333.3 103
• 333.3 100 or just 333.3

## How to simplify such an expression...

Dear all

I have such an expression in the file (test.mw). Obviously it is not a simple form. 10should be cancelled both in denominator and nominator. I have applied the function simplify(). However, it doesn't work.  I hope someone can do me a favor. That will help me a lot. Thanks

## Show value in scientific notation...

Hey

I have a simple question.

In maple - when working with Ohm's Law.

Maple know how to calculate with e, but how can I show the result

I have calculated the following calculation:

(2e-4)/2

Maple returns the result:0.0001000000000

How do I maple show the result as 1e-4?

## What's with MTM[sort]?...

It took me a while to figure out what was causing this unusual sort result;

I loaded the MTM package because I want to convert numbers to integers for indexing. This sort result seem like it could be a bug.

 Sort a List of Floats  =  =  =  =  =  =

## Need simplified answer as float...

 (1)

 (2)

Ramakrishnan V

rukmini_ramki@hotmail.com

## How to find the w and phi?...

1.

assume there are 3 real number or floating number a, b, c

how to find the w and phi in

a = sin(w*t1 + phi)

b = sin(w*t2 + phi)

c = sin(w*t3 + phi)

where w and phi are the same in above 3 equations, only different in t1, t2, t3

2.

same as above , how to find w, apha and beta in below if there are a, b, c

a = alpha*cos(w*t) + beta*sin(w*t)

b = alpha*cos(w*t) + beta*sin(w*t)

c = alpha*cos(w*t) + beta*sin(w*t)

## Exponents to floating point...

Maple 15

eq:=1/2*x^(1/2) + 1/13*x^(1/3) + 1/26*x^(45/37);
evalf(eq);

The exponents are still fractions.  I want to have floating point exponents.

0.5*x^0.500000 + 0.07692307692*x^0.333333 + 0.03846153846*x^1.216216216

How do I do this?

Tom Dean

## how to avoid the float(undefined)...

Hello,

Good day.

How to avoid float(undefined) for v3, v4,v5 in this problem.

## Solving for function of float...

To me the following behavior of solve is surprising:

restart;
solve(f(0.5)=7,f(0.5)); #Output NULL
solve(f(1/2)=7,f(1/2)); #Output as expected 7

Debugging solve suggested to me that the following might work
solve(f(0.5)=7,f(1/2));
and indeed it did (outout the float 7.).
This behavior seems to have started in Maple 10. I checked Maple V,R3 and several other old versions including Maple 9.5. All behaved as I would have expected. MapleV,R3 gave the float 7. in the first case, the other the integer 7.
I take this to be a bug and shall file an SCR.

## Eigenvectors of a big matrix...

Hi there

I have have a 18*18 matrix which almost each of its element are in symbolic form. Now I need to have all of its eigenvectors. Unfortunately when I use the "Eigenvalues()" function in maple i got nothing. In fact I got the error which comes below.

Error, (in content/polynom) general case of floats not handled

I need to know if there's a solution to eliminate the error? If not, what can I do to determine the eigenvectors and eigenvalues in symbolic form?

## Solving symbolic/numerical simultaneous equations?...

Hi,

I need to solve systems of numerical equations. I encountered a problem, where one of the parameters (tau[p3]) become FREE, see Maple worksheet attached.

That was clearly not expected.

I spent about 40 mintues to inspect what the problem is, eventually, I find that fsolve works perfectly.

Though fsolve would be the "first" choice for solving floating point problems. I really dont see why the simple "solve" syntax can not work. It is acting strange. And why is *tau[p3]*  FREE, not the others?

Could this be a bug? Or maybe is just WRONG to use solve?

Casper

solve-fsolve.mw

## Error, (in f) unable to store .......................

Hello Hello everybody
I have to solve the following differential equation numerically

 > restart:with(plots):
 > mb:=765 : mp:=587 : Ib:=76.3*10^3 : Ip:=7.3*10^3 : l:=0.92 : d:=10: F:=490: omega:=0.43 :
 > eq1:=(mp+mb)*diff(x(t),t$2)+mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(theta(t),t$2)+mp*l*cos(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*sin(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*sin(alpha(t)+theta(t)))-F*sin(omega*t)=0;  (1)  > eq2:=(mp+mb)*diff(z(t),t$2)-mp*d*(sin(theta(t)+alpha(t))+sin(theta(t)))*diff(theta(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(alpha(t),t$2)+mp*(d*diff(theta(t),t)^2*cos(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*cos(alpha(t)+theta(t)))+9.81*(mp+mb)-F*sin(omega*t)=0;
 (2)
 > eq3:=mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(x(t),t$2)-mp*(l*sin(theta(t)+alpha(t))+d*sin(theta(t)))*diff(z(t),t$2)+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+[Ip+mp*l^2+mp*d*l*cos(alpha(t))]*diff(alpha(t),t$2)-mp*sin(alpha(t))*(l*d*diff(alpha(t),t)^2-l*d*(diff(alpha(t),t)+diff(theta(t),t))^2)+mp*9.81*l*sin(alpha(t)+theta(t))+mp*9.81*d*sin(theta(t))=0;
 (3)
 > eq4:=mp*l*cos(alpha(t)+theta(t))*diff(x(t),t$2)-mp*l*sin(alpha(t)+theta(t))*diff(z(t),t$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(theta(t),t$2)+(Ip+mp*l^2)*diff(alpha(t),t$2)-mp*9.81*l*sin(alpha(t)+theta(t))+l*d*mp*diff(theta(t),t\$1)^2*sin(alpha(t))=0;
 (4)
 > CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;
 (5)
 > solution:=dsolve([eq1,eq2,eq3,eq4, CI],numeric);
 Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

I don't know why it says : Error, (in f) unable to store '[0.]/(0.17571268341557e16+[-0.25659510610770e15])' when datatype=float[8]

Help pleaase!

thank you !!!

## Round Matrix with non-numeric elements...

I wrote a procedure which rounds floats to a specified precision. I would like to apply it to a Matrix/List/Array/Vector that contains non-numeric cells as well as floats. I'm stuck at the type-checking stage.

# Round0 works on floats and lists and Matrices of floats:
restart;
Round0 := proc(x,n::integer:=1)
parse~(sprintf~(cat("%.",n,"f"),x));
end proc:

Round0(1.23456789);
1.2

Round0([1.23456789,9.87654321],2);
[1.23, 9.88]

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