It won't cause a recursion error. If we define a helper function to just do
the 'multiply DCM with the column vector' part, then that's all that we
will have to call to convert the Pos vector of B wrt A, in terms of A
(since they won't contain coordinate variables).
Hence, the actual 'express' function will call this helper function
twice...once in the first step, second time while converting pos vector of
B wrt A in terms of A.
On Wed, Jul 31, 2013 at 10:43 PM, Prasoon Shukla
<prasoon92.i...@gmail.com>wrote:
> Sorry for the late reply. Was busy with assignments.
>
> Anyway, so here's how we can proceed with this. First, we need to have all
> the base vectors and base scalars changed to rectangular coordinates. That
> I think, will be easy using the methods that I have written.
>
> Next comes the conversion of base vectors, as you've said, to the
> coordinate system in which we expect the result. That can be done as well -
> though I don't quite understand what you mean by 'separate to n-tuples with
> measures of basis vectors'. Do you want me to collect the coefficients of
> the base vectors? And this will need to be done for every coordinate system.
>
> So if
> v = c0.x * c1.e_y + c0.y * c1.e_z + c1.x * c0.e_x
> for examples, then, we separate as follows:
> { c0: (c1.x, 0, 0),
> c1: (0, c0.x, c0.y) }
> where the n-tuples represent the coefficients of e_x, e_y and e_z. Is this
> what you meant?
>
> If so, I'll proceed to multiply the matrices with DCMs and get measure
> numbers in the required frame - albeit in the old frames. Then, I should
> proceed to change these measure numbers to required coordinate systems as
> well. Right?
>
> Anyway, we can calculate Pos_vect of B wrt A = Pos_vect of B - Pos_vect of
> A as well, I think. But, there will be a problem when converting these
> vectors to other coordinate systems. This will cause a recursion error
> (maximum depth) since express will call to itself. So, that is a problem
> still.
>
> So, is this how I should proceed?
>
>
> On Wednesday, July 31, 2013 11:22:57 AM UTC+5:30, Gilbert Gede wrote:
>
>> I think you should split the operation into 2 steps: 1) expression of
>> basis vectors in new frame and 2) expression of coordinates in new frame.
>> This way, if the user only wants to do one or the other, they are able to.
>>
>> I think you should have the order for the complete re-expression being 1)
>> and then 2). I would separate the _basis vectors_ by frame, into n-tuples
>> of the measure numbers, then put those measure numbers in a (n x 1) Matrix,
>> and multiply the proper DCM by that measure number matrix, giving you
>> another Matrix of the measure numbers in the new frame. Some things will
>> cancel out, so I think it's better to do this step on all a frame's basis
>> vectors together.
>>
>> Next, what Sachin posted for the coordinate transformation ([vector of
>> A's vars] = [Pos-vector of B wrt A] + DCM(A, B) * [vector of B's vars]) is
>> mostly correct - I would clarify that [Pos-vector of B wrt A] is:
>> Matrix([dot(p_bo_ao.express(A)**, bv) for bv in A.basis_vectors()]).
>> Again, this is why I would do the basis expression first, so you can do
>> this expression of the position vector without issue.
>>
>> Does that help to clarify things?
>>
>> -Gilbert
>>
>>
>>
>>
>> On Tue, Jul 30, 2013 at 12:34 PM, Sachin Joglekar <srjogl...@gmail.com>wrote:
>>
>>> Ya, I agree quite a bit of handling-the-symbols would be required.
>>> Maybe, we could cache the relationships (dicts) between coordinate
>>> variables of different frames?
>>> Then, when 'express' is called, just iterate through the atoms of the
>>> vector expression and note the systems whose variables we come across?
>>> About the validity, I had discussed this method with Gilbert in the
>>> past, but I guess they should confirm this before you go ahead.
>>>
>>>
>>> On Wed, Jul 31, 2013 at 12:14 AM, Sachin Joglekar
>>> <srjogl...@gmail.com>wrote:
>>>
>>>> You may want to use the method I used while hacking the old mechanics
>>>> module to do the kind of re-expression we want to achieve. say a vector v
>>>> from frame A to frame B
>>>> First, we need to calculate the coordinate variables of frame A in
>>>> terms of those of B.
>>>> We can do this using -
>>>> [vector of A's vars] = [Pos-vector of B wrt A] + DCM(A, B) * [vector of
>>>> B's vars]
>>>> In above equation, don't take the LHS as a 'vector field'. It's just a
>>>> column matrix with the respective symbols denoting coordinate variables of
>>>> A.
>>>> Comparing the entries in LHS and RHS will help you contrust a dict
>>>> mapping A.x, A.y and A.z in terms of B.x, B.y, B.z
>>>>
>>>> Use the sympy subs method on v to remove A.x, A.y and A.z from its
>>>> expression. Suppose we now get v1
>>>> Then just do
>>>> [final vector] = DCM(A, B) * [v1]
>>>>
>>>> The above will give the required re-expressed vector.
>>>>
>>>> For the above method to work, you *just* need to separate the vector
>>>> into components based on the basis _vectors_, not scalars. Since we are
>>>> going to 'subs' them, their occurences don't matter. And according to me,
>>>> thats what separate should do- just think of basis vectors. Then use the
>>>> above algo on each component thus found out to get the final result. You
>>>> can try this with an example and confirm the validity.
>>>>
>>>> @stefan, @gilbert, am I correct?
>>>>
>>>>
>>>> On Tue, Jul 30, 2013 at 11:46 PM, Prasoon Shukla
>>>> <prasoon...@gmail.com>wrote:
>>>>
>>>>> @All: This is a cry for help.
>>>>>
>>>>> I am completely stumped at the *express* method. The implementation
>>>>> that I had before had a flaw that I hadn't noticed until now (until
>>>>> Gilbert's PR on by branch). Anyway, let me try to describe the situation.
>>>>>
>>>>> Initially, I had an separate method that would take a vector and
>>>>> return it separated by coordinate systems in dictionary form. To my
>>>>> chagrin, this kind of separation cannot always work. Consider two
>>>>> coordinate systems, c0 and c1, both rectangular. Let us have a vector, v.
>>>>>
>>>>> v = c0.x * c1.e_y
>>>>> express
>>>>> Obviously, this cannot be separated into vectors separated by
>>>>> coordinate systems. This is the case I wasn't considering when I wrote the
>>>>> express method last. And that's why, I need to rewrite a new express
>>>>> method.
>>>>>
>>>>> I have been thinking of how to implement this but I'm getting nowhere.
>>>>> I do have one way, that I think might work and am currently writing the
>>>>> code for it. But, I'm not at all too sure of it.
>>>>>
>>>>> I think that by now, all three of you have a fair idea of the code.
>>>>> Please suggest an algorithm to accomplish this.
>>>>>
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>>>>>
>>>>
>>>>
>>>
>>
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