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From: Joe Riel <joer@san.rr.com>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Vectors in the Physics package
Date: Fri, 14 Nov 2014 07:38:35 -0800
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rouben@shadow.(none) (Rouben Rostamian) writes:

> In article <m44dev$2lb$1@news.albasani.net>,
> none) (Rouben Rostamian <rouben@shadow.> wrote:
>>In article <87oasakjdd.fsf@san.rr.com>, Joe Riel  <joer@san.rr.com> wrote:
>>>rouben@shadow.(none) (Rouben Rostamian) writes:
>>>
>>>> This is a question about Physics[Vectors] package.
>>>>
>>>> Let's say we want to plot the helix v = [ cos(t), sin((t), t], where
>>>> v is given as a Physics Vector.  Here is what I do:
>>>>
>>>>     restart;
>>>>     with(Physics[Vectors]):
>>>>     Setup(mathematicalnotation=true):
>>>>     with(plots):
>>>>     v_ := cos(t)*_i + sin(t)*_j + t*_k;
>>>>     spacecurve( [ Component(v_,1), Component(v_,2), Component(v_,3) ],
>>>>        t=0..4*Pi);
>>>>
>>>> This works fine, but the extraction of the components in the last
>>>> line looks too clunky to me.  Alternatively we may do
>>>>
>>>>     spacecurve( [ v_ . _i, v_ . _j, v_ . _k ], t=0..4*Pi);
>>>>
>>>> which is a bit shorter, but I suspect that I am missing something
>>>> more basic.  I tried convert(v_, list) and convert(v_, Vector)
>>>> but did not get anything useful.
>>>>
>>>> So the question is one of:
>>>> a) Is there a command to convert v_ to a list or a Vector?
>>>> b) Is there some other way to plot the spacecurve given by v_?
>>>
>>>You could do
>>>
>>>  basis := [_i,_j,_k]:
>>>
>>>then
>>>
>>>  spacecurve( v_.basis, t=0..4*Pi);
>>>
>>>does what you want.
>>
>>Perfect!  Thanks for your valuable help, as always.
>
> Oops, I spoke too soon.  Actually I spoke before trying
> the suggested solution.  In Maple 17 and 18 I get:
>
>   restart;
>   with(Physics[Vectors]):
>   Setup(mathematicalnotation=true):
>   with(plots):
>   v_ := cos(t)*_i + sin(t)*_j + t*_k:
>   basis := [_i,_j,_k]:
>   spacecurve( v_.basis, t=0..4*Pi);
>
> Error, (in plots/spacecurv) first argument must be array, rtable, list or set
>
> Perhaps there is a typo in the suggested solution.  

Not a typo, but I only tested it on a beta version of Maple.
In 18 you can can do map(`.`,basis,v_), which isn't as nice.

-- 
Joe Riel