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Cheers!

I'm having a problem with my student work, about to have a solution of 6 equations... Can help me in this file? i dont know how to solve this... this had-me a null solve...

 

 


Thanks for the help =)

restart

M1 := 0.15e5;

0.15e5

 

0.60e5

 

0

 

0.12e5

 

21000.00000

 

3

 

1

 

2.5

 

1

 

3

(1)

`σadm` := 175*10^6;

175000000

 

(1/300000)*L

 

210000000000

(2)

Atria := (3.5*12)/(LBC+LCD)

12.00000000

(3)

Ctria := LAB+LBC+(1/3)*(2*(LCD+LDE))

6.333333334

(4)

AiXil := Atria*Ctria

76.00000001

(5)

C := AiXil/Atria

6.333333334

(6)

``

``

``

SumFX := FAx;

FAx

(7)

SumFY := FAy+FCy+FEy-F5-QTria;

FAy+FCy+FEy-81000.00000

(8)

SumMA := FCy*(LAB+LBC)-F5*(LAB+LBC)+FEy*(LAB+LBC+LCD+LDE)+M1-MA-QTria*Ctria;

4*FCy-358000.0000+7.5*FEy-MA

(9)

NULL

``

``

EIYac := EIYo+`EIθo`*x+M1*(x+0)^3/factorial(3);

EIYo+`EIθo`*x+2500.000000*x^3

(10)

EIYce := EIYac+FCy*(x-4)^3/factorial(3)-F5*(x-4)^3/factorial(3)-q5*(x-4)^5/((3.5)*factorial(5));

EIYo+`EIθo`*x+2500.000000*x^3+(1/6)*FCy*(x-4)^3-10000.00000*(x-4)^3-28.57142857*(x-4)^5

(11)

EIYef := EIYce+FEy*(x-7.5)^3/factorial(3)+(1/3)*q5*(x-7.5)^5/factorial(5);

EIYo+`EIθo`*x+2500.000000*x^3+(1/6)*FCy*(x-4)^3-10000.00000*(x-4)^3-28.57142857*(x-4)^5+(1/6)*FEy*(x-7.5)^3+33.33333333*(x-7.5)^5

(12)

`EIθac` := diff(EIYac, x);

`EIθo`+7500.000000*x^2

(13)

`EIθce` := diff(EIYce, x);

`EIθo`+7500.000000*x^2+(1/2)*FCy*(x-4)^2-30000.00000*(x-4)^2-142.8571428*(x-4)^4

(14)

`EIθef` := diff(EIYef, x);

`EIθo`+7500.000000*x^2+(1/2)*FCy*(x-4)^2-30000.00000*(x-4)^2-142.8571428*(x-4)^4+(1/2)*FEy*(x-7.5)^2+166.6666666*(x-7.5)^4

(15)

``

Mac := diff(`EIθac`, x);

15000.00000*x

(16)

Mce := diff(`EIθce`, x);

-45000.00000*x+FCy*(x-4)+240000.0000-571.4285712*(x-4)^3

(17)

Mef := diff(`EIθef`, x);

-45000.00000*x+FCy*(x-4)+240000.0000-571.4285712*(x-4)^3+FEy*(x-7.5)+666.6666664*(x-7.5)^3

(18)

``

Vac := diff(Mac, x);

15000.00000

(19)

Vce := diff(Mce, x);

-45000.00000+FCy-1714.285714*(x-4)^2

(20)

Vef := diff(Mef, x);

-45000.00000+FCy-1714.285714*(x-4)^2+FEy+1999.999999*(x-7.5)^2

(21)

``

x := 0:
``

`EIθo` = 0

 

EIYo = 0

(22)

x := 4:

EIYo+4*`EIθo`+160000.0000

(23)

x := 7.5:

EIYo+7.5*`EIθo`+610931.2500+7.145833333*FCy

(24)

SOL := solve({CF1, CF2, CF3, CF4, SumFY, SumMA}, {EIyo, FAy, FCy, FEy, MA, `EIyθo`});

"SOL:="

(25)

``

NULL

``

 

Download Equacoes_universais_T12_-_4.mwEquacoes_universais_T12_-_4.mw

 

Symbolic sequences enter in various formulations in mathematics. This post is about a related new subpackage, Sequences, within the MathematicalFunctions package, available for download in Maplesoft's R&D page for Mathematical Functions and Differential Equations (currently bundled with updates to the Physics package).

 

Perhaps the most typical cases of symbolic sequences are:

 

1) A sequence of numbers - say from n to m - frequently displayed as

n, `...`, m

 

2) A sequence of one object, say a, repeated say p times, frequently displayed as

 "((a,`...`,a))"

3) A more general sequence, as in 1), but of different objects and not necessarily numbers, frequently displayed as

a[n], `...`, a[m]

or likewise a sequence of functions

f(n), `...`, f(m)

In all these cases, of course, none of n, m, or p are known: they are just symbols, or algebraic expressions, representing integer values.

 

These most typical cases of symbolic sequences have been implemented in Maple since day 1 using the `$` operator. Cases 1), 2) and 3) above are respectively entered as `$`(n .. m), `$`(a, p), and `$`(a[i], i = n .. m) or "`$`(f(i), i = n .. m)." To have computer algebra representations for all these symbolic sequences is something wonderful, I would say unique in Maple.

Until recently, however, the typesetting of these symbolic sequences was frankly poor, input like `$`(a[i], i = n .. m) or ``$\``(a, p) just being echoed in the display. More relevant: too little could be done with these objects; the rest of Maple didn't know how to add, multiply, differentiate or map an operation over the elements of the sequence, nor for instance count the sequence's number of elements.

 

All this has now been implemented.  What follows is a brief illustration.

restart

First of all, now these three types of sequences have textbook-like typesetting:

`$`(n .. m)

`$`(n .. m)

(1)

`$`(a, p)

`$`(a, p)

(2)

For the above, a$p works the same way

`$`(a[i], i = n .. m)

`$`(a[i], i = n .. m)

(3)

Moreover, this now permits textbook display of mathematical functions that depend on sequences of paramateters, for example:

hypergeom([`$`(a[i], i = 1 .. p)], [`$`(b[i], i = 1 .. q)], z)

hypergeom([`$`(a[i], i = 1 .. p)], [`$`(b[i], i = 1 .. q)], z)

(4)

IncompleteBellB(n, k, `$`(factorial(j), j = 1 .. n-k+1))

IncompleteBellB(n, k, `$`(factorial(j), j = 1 .. n-k+1))

(5)

More interestingly, these new developments now permit differentiating these functions even when their arguments are symbolic sequences, and displaying the result as in textbooks, with copy and paste working properly, for instance

(%diff = diff)(hypergeom([`$`(a[i], i = 1 .. p)], [`$`(b[i], i = 1 .. q)], z), z)

%diff(hypergeom([`$`(a[i], i = 1 .. p)], [`$`(b[i], i = 1 .. q)], z), z) = (product(a[i], i = 1 .. p))*hypergeom([`$`(a[i]+1, i = 1 .. p)], [`$`(b[i]+1, i = 1 .. q)], z)/(product(b[i], i = 1 .. q))

(6)

It is very interesting how much this enhances the representation capabilities; to mention but one, this makes 100% possible the implementation of the Faa-di-Bruno  formula for the nth symbolic derivative of composite functions (more on this in a post to follow this one).

But the bread-and-butter first: the new package for handling sequences is

with(MathematicalFunctions:-Sequences)

[Add, Differentiate, Map, Multiply, Nops]

(7)

The five commands that got loaded do what their name tells. Consider for instance the first kind of sequences mentione above, i.e

`$`(n .. m)

`$`(n .. m)

(8)

Check what is behind this nice typesetting

lprint(`$`(n .. m))

`$`(n .. m)

 

All OK. How many operands (an abstract version of Maple's nops  command):

Nops(`$`(n .. m))

m-n+1

(9)

That was easy, ok. Add the sequence

Add(`$`(n .. m))

(1/2)*(m-n+1)*(n+m)

(10)

Multiply the sequence

Multiply(`$`(n .. m))

factorial(m)/factorial(n-1)

(11)

Map an operation over the elements of the sequence

Map(f, `$`(n .. m))

`$`(f(j), j = n .. m)

(12)

lprint(`$`(f(j), j = n .. m))

`$`(f(j), j = n .. m)

 

Map works as map, i.e. you can map extra arguments as well

MathematicalFunctions:-Sequences:-Map(Int, `$`(n .. m), x)

`$`(Int(j, x), j = n .. m)

(13)

All this works the same way with symbolic sequences of forms "((a,`...`,a))" , and a[n], `...`, a[m]. For example:

`$`(a, p)

`$`(a, p)

(14)

lprint(`$`(a, p))

`$`(a, p)

 

MathematicalFunctions:-Sequences:-Nops(`$`(a, p))

p

(15)

Add(`$`(a, p))

a*p

(16)

Multiply(`$`(a, p))

a^p

(17)

Differentation also works

Differentiate(`$`(a, p), a)

`$`(1, p)

(18)

MathematicalFunctions:-Sequences:-Map(f, `$`(a, p))

`$`(f(a), p)

(19)

MathematicalFunctions:-Sequences:-Differentiate(`$`(f(a), p), a)

`$`(diff(f(a), a), p)

(20)

For a symbolic sequence of type 3)

`$`(a[i], i = n .. m)

`$`(a[i], i = n .. m)

(21)

MathematicalFunctions:-Sequences:-Nops(`$`(a[i], i = n .. m))

m-n+1

(22)

Add(`$`(a[i], i = n .. m))

sum(a[i], i = n .. m)

(23)

Multiply(`$`(a[i], i = n .. m))

product(a[i], i = n .. m)

(24)

The following is nontrivial: differentiating the sequence a[n], `...`, a[m], with respect to a[k] should return 1 when n = k (i.e the running index has the value k), and 0 otherwise, and the same regarding m and k. That is how it works now:

Differentiate(`$`(a[i], i = n .. m), a[k])

`$`(piecewise(k = i, 1, 0), i = n .. m)

(25)

lprint(`$`(piecewise(k = i, 1, 0), i = n .. m))

`$`(piecewise(k = i, 1, 0), i = n .. m)

 

MathematicalFunctions:-Sequences:-Map(f, `$`(a[i], i = n .. m))

`$`(f(a[i]), i = n .. m)

(26)

Differentiate(`$`(f(a[i]), i = n .. m), a[k])

`$`((diff(f(a[i]), a[i]))*piecewise(k = i, 1, 0), i = n .. m)

(27)

lprint(`$`((diff(f(a[i]), a[i]))*piecewise(k = i, 1, 0), i = n .. m))

`$`((diff(f(a[i]), a[i]))*piecewise(k = i, 1, 0), i = n .. m)

 

 

And that is it. Summarizing: in addition to the former implementation of symbolic sequences, we now have textbook-like typesetting for them, and more important: Add, Multiply, Differentiate, Map and Nops. :)

 

The first large application we have been working on taking advantage of this is symbolic differentiation, with very nice results; I will see to summarize them in a post to follow in a couple of days.

 

Download MathematicalFunctionsSequences.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Am I right that using methods of the 1-forms (that implemented in liesymm or DESOLV), we can always generate determining equations for ODE, that solved for highest derrivative?

We find recent applications of the components applied to the linear momentum, circular equations applied to engineering. Just simply replace the vector or scalar fields to thereby reasoning and use the right button.

 

Momento_Lineal_y_Circular.mw

(in spanish)

Atte.

L.AraujoC.

y'(t)=1-y'(t-y(t)^2 /4),      t>=0

with initial function

y(t)=1+t,   0<=t<=1

please solve

Developed and then implemented with open code components. It is very important to note this post is held for students of civil engineering and mechanics. Using advanced mathematical concepts to concepts in engineering.

Metodos_Energeticos_full.mw

(in spanish)

Atte.

L.Araujo.C

 

 

 

 

 

Hi all.

I am using Maple2015.

I typed in as input y=x/sqrt(1-x^2).

I hit enter.  The output is:

 y=x/sqrt(1-x^2)

I know the 2 answers are equivalent.

My question is why did Maple swap 1-x^2 to -x^2+1???

Any advice to swap it back would be greatly appreciated.

Hello,

I need to prepare for a final exam for a introdutory computer science course in Maple.
My professor gives us mutliple choice questions, short answer questions and wiritng some codes.

what is the most efficient way to study for my final exam? or how should i study for an computer science exam. I am not really use to preparing for such a course. 

Are there any websites that i can practice multiple choice questions?

I would appreciate any advice.

 

Thank you very much.

Here we have a very brief introduction to the use of embedded components, but effective for the study of the polynomials in operations and some products made with maple 2015 to strengthen and raise the mathematics today.

 

Operaciones_con_Polinomios.mw

(in spanish)

Atte.

L.AraujoC.

How to avoid the error described in the title

 

Here we have an application to understand how algebraic expressions, calculating degrees relative abosulutos polynomial operations and introduction to work.Here we have an application to understand how algebraic expressions, calculating degrees relative abosulutos polynomial operations and introduction to work.

 

Grados_de_Polinomios.mw

(in spanish)

Atte.

L.AraujoC.

 

 

Hi, I build my simulation system in MapleSim, using the module 'Stepper Permanent Magnet' like this

 

But when I run this system, I get the followiing error:

System is underdetermined

 

When I delete the part about 'Stepper Permanent Magnet', the system runs well.

How to solve this problem? How to use 'Stepper Permanent Magnet'?

The Help file of MapleSim cannot proviod such help information.

Thank you.

 

 

 

 

Hi,

I was trying to find the solution for two theta variables in a couple of simultaneous equations (infact this is an iverse kinematics problem for a two link system pendulum).
The following are the initial inputs/equations to be manipulated:


Then I use the folowing command to rearrange for the theta values which I am after:

which gives me the result:

This is all fine until I give in values for l1, l2, x and y:


results:

I have a RootOf in there with a _Z term poping up here and there. I know that this configuration of the two link mechanism in fact dows have a solution and that these numbers are reasonable. Thus I have three questions:

Why does this happen?
What does the "signum" mean here?
how do I go about getting the nummerical values?

Many thanks,
- pjf

the calculation is like the following command, the result in the picture

restart;
with(VectorCalculus);
SetCoordinates(spherical[r, theta, phi]);
Fv := rho*VectorField(`<,>`(v[r](r, theta, phi), v[theta](r, theta, phi), v[phi](r, theta, phi)));
Divergence();
Divergence(Fv);

divergence

 

1) when the Divergence act on the Fv, then it will be expanded, which is lengthy and not like most book's formulation , especially when I want to continue for a Conversation law like in fluid mechanics, this will be too long and a messy for later check.

could there be a way to not expand this result, just as the eq(3) like.

2) when I want to calculate the Divergence of Fv, I must construct a VectorField at first, but this is in components way, is there a quick way for Vector Field Function

 

I want to make the model which moves along the specific direction (translational), So I used the "prismatic joint" to give the direction that I want to enforce. However, "Prismatic joint" only offers the direction along the "X", "Y", and "Z" axes though I want to give other direction.

 

Is there any way to give the specific direction (vector) to make my model move in that way ?

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