On Sun, May 15, 2011 at 1:40 AM, Luke <[email protected]> wrote:
> Gilbert,
> I prefer this notation:
>
>>>> B = ReferenceFrame('B')
>
> and then to access the basic vectors of that frame, to use one of the
> following approaches:
>
> B.x, B.y, B.z or, B.i, B.j, B.k
>
> You could view the ReferenceFrame class as a container object for the
> basis vectors and implement the __iter__() method to iterate over the
> basis vectors in the following way:
>
> v = a*B.i + b*B.j + B.k
> for basisvector in B:
> dot(v, basisvector)
>
> Since we are restricting ourself to basis vectors in R^3, we probably
> don't need all the other methods typical of a container object, I
> think __iter__() would be enough.
>
> My vote is to go with the ijk or xyz syntax and not use the
> __getitem__() method that allows for B[1]. This will mean some work
> to change things from how they are currently implemented in PyDy, but
> I think the syntax is cleaner and more concise. What do other people
> think about this?
My preference is the ijk syntax so
v = a*B.i + b*B.j + B.k
works fine for me. Being able to convert v to a 1x3 matrix would be
nice too. In the event you want to work with it as a linear algebra
vector or as a tensor would be useful. So, if you could say
lv = Vector(v)
to convert v to a 1x3 vector.
I'd prefer not to use xyz since that's typically used solely for
Cartesian coordinates.
>
> Another thing to think about though is how you will print the basis
> vectors, both to the screen and to LaTeX. Currently, PyDy prints
> UnitVectors as b1>, b2>, b3>, and it uses unicode to make the color
> bright so you can distinguish UnitVectors from the scalar multiplier.
> For LaTeX printing, this I think should be \boldsymbol{b}_{1},
> \boldsymbol{b}_x or \boldsymbol_{i}. If you go with the ijk syntax,
> bi>, bj>, bk> might work but in most physics/math books I have seen
> they typically only use \hat{\boldsymbol{i}}, etc, and typically this
> is in settings where you don't have many different reference frames to
> distinguish between, so the syntax isn't ambiguous. On the other
> hand, I have seen \boldsymbol{b}_x, etc, so perhaps this might be more
> common and familiar to some users? It is a pretty minor difference,
> so I say you pick one you think is most likely to appeal to the widest
> audience and stick with it. This might also be something that could
> have a default value, but could be customized -- I have seen
> subscripts of ijk, xyz, 012, or 123 in various classical mechanics
> literature.
what about \vec{i} which is quite common. I use a variant with the
vector on the bottom instead of the top, but I created a command to
get the style I wanted. The advantage of using \vec{i} is that it's
simple to use regular expressions to switch to another command and
easy to switch by hand if necessary. I don't use I think you'd want
\mathbf{b} instead of \boldsymbol, though. \boldsymbol seems to be
used for symbols, while \mathbf is a math bold font for characters.
>
> Do any of the physics people out there have thoughts on what syntax
> would be nicest for physics students? We definitely want to keep the
> syntax familiar to that potential user base, but we also need to make
> sure we can accommodate many different reference frames which is
> common in multibody dynamics.
>
\vec with i,j,k as the basis vectors is what's taught in all the
engineering physics courses I know of at my university. I've been a TA
for all physics courses but the EM course in my department (and been
friends with various people in other departments). We've tended to use
\mathbf{v} for the vector of magnitudes that multiply the basis
vectors. So, you could have
\vec{v} = [\vec{i} \vec{j} \vec{k}] [v_1 v_2 v_3]^T
where the last vector is \mathbf{v} (and all are assumed to be a
column vector). I just wrote them as row vectors for e-mail
convenience.
Cheers,
Tim.
--
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://about.me/tjlahey
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