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These are replies submitted by sarra


Many thanks for your remarks, unfortunately the commutator [x,y] different to zero since we work non-commutative element and x , y denotes some operators 




many thanks for your help

It's the right answer that I want


I think now all equations are well writt, so how can we get the matrix using Generatematrix

many thanks

I agree with you, two lines in the code are modified according to your remark. Many thanks.


First, thank you for your remarks, i really appreciate your comments.

I removed the loop if ... and .. then because in that loop we have only one equation.

I have modified the code and you will see that mow, the number of variable equal the number of equation. I hope now it's correct



One again, thank you for the code, it's very nice

Please find attached some remarks added in the attached file.
You begin your numerotation with k=0..
we have 4 equations defined using in the code using (if  ... and ..  then ) those equations are not included in your numerotation, so if you add the four equation defined in maple code using if ... and ...then we have the same number of equations as the number of variables.

@Rouben Rostamian  

Many thanks, I try to see the missing equations..

The equations are listed in the maple code.

How can I give a name each equation in each loop, and then use generatematrixto get the full matrix

The code work well, without any error, but how can I get the matrix generated by all equation in the code. Thanks



Thank you, but I think that the loop defined  using command maple is wrong. 

@Rouben Rostamian  

I agree with you. But I thank as we have the coordinate of the normal of the top plate N and A and B can be seen as two unit vectors on the top plate such N=A cross B is there any method may be to deduce A and B  or using Euler angle or something else. 

If I can find the three different angles alpha, beta and gamma then the results is obtained




Position of the moving platform can be expressed using a matrix defined by the roll pitch and yaw angles i.e. we will use the following matrix

R := matrix([[cos(beta)*cos(gamma), cos(gamma)*sin(alpha)*sin(beta)-cos(alpha)*sin(gamma), sin(alpha)*sin(gamma)+cos(alpha)*cos(gamma)*sin(beta)], [cos(beta)*sin(gamma), cos(alpha)*cos(gamma)+sin(alpha)*sin(beta)*sin(gamma), cos(alpha)*sin(beta)*sin(gamma)-cos(gamma)*sin(alpha)], [-sin(beta), cos(beta)*sin(alpha), cos(alpha)*cos(beta)]]);


R := Matrix(3, 3, {(1, 1) = cos(beta)*cos(gamma), (1, 2) = cos(gamma)*sin(alpha)*sin(beta)-cos(alpha)*sin(gamma), (1, 3) = sin(alpha)*sin(gamma)+cos(alpha)*cos(gamma)*sin(beta), (2, 1) = cos(beta)*sin(gamma), (2, 2) = cos(alpha)*cos(gamma)+sin(alpha)*sin(beta)*sin(gamma), (2, 3) = cos(alpha)*sin(beta)*sin(gamma)-cos(gamma)*sin(alpha), (3, 1) = -sin(beta), (3, 2) = cos(beta)*sin(alpha), (3, 3) = cos(alpha)*cos(beta)})


we define the vector L=R*PL_T+P-LB

and the length of the edge will be the norm of L

My questions:

The value of different angles alpha, beta, gamma.????

How can we use the normal to deduce some properties and determine the matrix 







Maybe for the fourth condition can be given in the reference of bottom plane,i.e. X Y plane 

@Rouben Rostamian  

Thank you for your help

Assume the following (the units of all lengths are in centimetres):


·       P is of length 13 and displaced in the Y direction by 10 degrees from the vertical (Z axis)

·       N is displaced in the X direction by 18 degrees from the vertical (Z axis)

·       LB is position [7 5] from the bottom plate centre in the XY plane

·       LT is in position [3.5 4.2] from the top-plate centre in the AB plane


First, thank you for your remarks.
So, as you say we are not able not determine a series expansion if we put the first argument to be non-numeric in the Hankel function.
So, the question is always can we find an approximation for large x and zeta is a small positive parameter ....I think it's not obvious but maye be can somelese find other stategies to give a clear answer  

HankelH1(x*(1+zeta), x);


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