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Re: Symbols in expression
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89099] Re: [mg89079] Symbols in expression
*From*: DrMajorBob <drmajorbob at att.net>
*Date*: Sun, 25 May 2008 06:27:35 -0400 (EDT)
*References*: <15605470.1211701065210.JavaMail.root@m08>
*Reply-to*: drmajorbob at longhorns.com
It all depends.
eqns = Array[r, 3] == {Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]} //
Thread;
Reduce[eqns, {u, v}]
will return MANY solutions (not shown here).
Wade through that thicket if you care to, but inspection yields a simpler
approach.
The third equation is easily solved:
Solve[eqns1[[-1]], v]
Solve::ifun: Inverse functions are being used by Solve, so some \
solutions may not be found; use Reduce for complete solution \
information. >>
{{v -> -ArcCos[r[3]]}, {v -> ArcCos[r[3]]}}
Dividing the first and second equations gives
sides = List @@@ eqns;
Solve[Equal @@ (sides[[1]]/sides[[2]]), u]
Solve::ifun: Inverse functions are being used by Solve, so some \
solutions may not be found; use Reduce for complete solution \
information. >>
{{u -> ArcCot[r[1]/r[2]]}}
That cover mosts cases, but you still have to decide what sign to give v
and what to do when r[2] and/or r[2] is zero. (Either way, the rule for u
gives an undefined result.)
Bobby
On Sun, 25 May 2008 02:22:00 -0500, <sigmundv at gmail.com> wrote:
> Dear all,
>
> Define, say,
>
> r = {Cos[u] Sin[v],Sin[u] Sin[v],Cos[v]}.
>
> How can I write a function, which takes r as an argument and returns a
> list {u,v}? If we defined r[u_,v_]:=... it could be achieved fairly
> easily using DownValues. But how can I achieve it in this case?
>
> Kind regards,
> Sigmund Vestergaard
>
>
--
DrMajorBob at longhorns.com
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