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Carl Love

Carl Love

28070 Reputation

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13 years, 31 days
Himself
Wayland, Massachusetts, United States
Contact Carl Love
My name was formerly Carl Devore.

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These are replies submitted by Carl Love

Can't view image...

Carl Love 28070
October 23 2013

I can't view your image. Please upload a worksheet, not an image.

It's the order of the derivatives...

Carl Love 28070
October 23 2013

The diff_table is symmetric, so it won't let you control the order of the derivatives: F[x,y] is identical to F[y,x]. Look closely at the order that it places the derivatives:

lprint(F[x,y]);
diff(diff(f(x, y, w, z, a, b), x), y)
lprint(F[x,b]);
diff(diff(f(x, y, w, z, a, b), b), x)

In the first case the F[x] is an integral part of the expression, and hence it can be substituted. In the second case it is not an integral part of the expression, and hence it cannnot be substituted.

Here's my results...

Carl Love 28070
October 22 2013
0 0

@Bendesarts Here are my results. Download the attached worksheet and run it on your system.


 

> 

restart
> 

kernelopts(version);

`Maple 16.00, X86 64 WINDOWS, Sep 16 2012, Build ID 773592`

 (1)
> 

constants := (`minus`({constants}, {gamma}))[]:
> 

P_1_0 := Matrix([`<,>`(cos(gamma(t)), -sin(gamma(t)), 0), `<,>`(sin(gamma(t)), cos(gamma(t)), 0), `<,>`(0, 0, 1)])

P_1_0 := Matrix(3, 3, {(1, 1) = cos(gamma(t)), (1, 2) = sin(gamma(t)), (1, 3) = 0, (2, 1) = -sin(gamma(t)), (2, 2) = cos(gamma(t)), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 (2)
> 

AG1_R1 := `<,>`((1/2)*r, 0, 0)

AG1_R1 := Vector(3, {(1) = (1/2)*r, (2) = 0, (3) = 0})

 (3)
> 

AG1_R0 := simplify(P_1_0.AG1_R1)

AG1_R0 := Vector(3, {(1) = (1/2)*cos(gamma(t))*r, (2) = -(1/2)*sin(gamma(t))*r, (3) = 0})

 (4)
> 

V_G1_R0 := map(diff, AG1_R0, t)

V_G1_R0 := Vector(3, {(1) = -(1/2)*sin(gamma(t))*(diff(gamma(t), t))*r, (2) = -(1/2)*cos(gamma(t))*(diff(gamma(t), t))*r, (3) = 0})

 (5)
> 

``

``


Download gamma.mw

Here's my results...

Carl Love 28070
October 22 2013

@Bendesarts Here are my results. Download the attached worksheet and run it on your system.


restart:

> 

kernelopts(version);

`Maple 16.02, X86 64 WINDOWS, Nov 18 2012, Build ID 788210`

constants:= ({constants} minus {gamma})[]:

`evalf/gamma`:= proc() end proc:

`evalf/constant/gamma`:= proc() end proc:

unprotect(gamma);

> 

P_1_0:=Matrix([<cos(gamma(t)),-sin(gamma(t)),0>,<sin(gamma(t)), cos(gamma(t)),0 >,<0, 0, 1>]);
> 

AG1_R1:=<(1/2)*r, 0, 0>;
> 

AG1_R0:=simplify(P_1_0.AG1_R1);
> 

V_G1_R0:=map(diff, AG1_R0, t);
> 

 

P_1_0 := Matrix(3, 3, {(1, 1) = cos(gamma(t)), (1, 2) = sin(gamma(t)), (1, 3) = 0, (2, 1) = -sin(gamma(t)), (2, 2) = cos(gamma(t)), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

AG1_R1 := Vector(3, {(1) = (1/2)*r, (2) = 0, (3) = 0})

AG1_R0 := Vector(3, {(1) = (1/2)*cos(gamma(t))*r, (2) = -(1/2)*sin(gamma(t))*r, (3) = 0})

V_G1_R0 := Vector(3, {(1) = -(1/2)*sin(gamma(t))*(diff(gamma(t), t))*r, (2) = -(1/2)*cos(gamma(t))*(diff(gamma(t), t))*r, (3) = 0})

> 

 


Download gamma.mw

Not listed as thread safe...

Carl Love 28070
October 22 2013

Physics is not listed at ?index,threadsafe , so it must be considered unsafe.

It works for me...

Carl Love 28070
October 22 2013
0 0

@Bendesarts It works for me in Maple 16. What error are you getting?

Note that MatrixVectorMultiply(A, B) can be shortened to simply A.B

It works for me...

Carl Love 28070
October 22 2013

@Bendesarts It works for me in Maple 16. What error are you getting?

Note that MatrixVectorMultiply(A, B) can be shortened to simply A.B

Example?...

Carl Love 28070
October 22 2013
0 0

@Bendesarts Would you please show me an example of it not working? With the above commands, I am able to do diff(gamma(t), t) and simplify(gamma(t)) with no problem.

Example?...

Carl Love 28070
October 22 2013

@Bendesarts Would you please show me an example of it not working? With the above commands, I am able to do diff(gamma(t), t) and simplify(gamma(t)) with no problem.

Attached file(s) missing...

Carl Love 28070
October 22 2013

There is no attached file on your question.

Sorry, didn't notice it....

Carl Love 28070
October 22 2013

@J4James Sorry, I didn't notice the attached file. I got it now.

Doesn't match what?...

Carl Love 28070
October 22 2013

What is it that the output doesn't match? Can you show a graph of the alternative?

siderels and sqrts...

Carl Love 28070
October 21 2013

It's an interesting problem. The simplified form that you got with solve andsubs contains sqrt(s[4]), even though the expressions to be simplified and the side relations are purely polynomial. The simplify-with-side-relations will never introduce sqrt like that. There may be some options though. I haven't been able to get it to work yet, but there may be a way where you change s[4] to s[4]^2.

Pedagogy...

Carl Love 28070
October 21 2013
0 0

Thanks for the addition. I had stretched out the computation for pedagogical reasons---to emphasize the linear algebra---thinking that the OP was taking a course in it.

Pedagogy...

Carl Love 28070
October 21 2013

Thanks for the addition. I had stretched out the computation for pedagogical reasons---to emphasize the linear algebra---thinking that the OP was taking a course in it.

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