Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2014

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Inverse function solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132651] Re: Inverse function solution
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Tue, 29 Apr 2014 01:32:50 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: l-mathgroup@wolfram.com
  • Delivered-to: mathgroup-outx@smc.vnet.net
  • Delivered-to: mathgroup-newsendx@smc.vnet.net
  • References: <20140428014444.9FBD16A4E@smc.vnet.net>

$Version


"9.0 for Mac OS X x86 (64-bit) (January 24, 2013)"


sol = Assuming[
  {-1 <= x <= 1, -1 <= y <= 1, C[1] == 0, C[2] == 0},
  Solve[{x == Cos[u], y == Cos[u + v]}, {u, v}] //
   Simplify]


{{u -> ArcTan[x, -Sqrt[1 - x^2]],
     v -> ArcTan[Sqrt[1 - x^2]*(x*y -
              Sqrt[(-1 + x^2)*(-1 + y^2)]),
         y - x^2*y + x*Sqrt[(-1 + x^2)*(-1 + y^2)]]},
   {u -> ArcTan[x, -Sqrt[1 - x^2]],
     v -> ArcTan[Sqrt[1 - x^2]*(x*y +
              Sqrt[(-1 + x^2)*(-1 + y^2)]),
         y - x^2*y - x*Sqrt[(-1 + x^2)*(-1 + y^2)]]},
   {u -> ArcTan[x, Sqrt[1 - x^2]],
     v -> ArcTan[x*y - Sqrt[(-1 + x^2)*(-1 + y^2)],
         -((y - x^2*y + x*Sqrt[(-1 + x^2)*(-1 + y^2)])/
              Sqrt[1 - x^2])]}, {u -> ArcTan[x, Sqrt[1 - x^2]],
     v -> ArcTan[Sqrt[1 - x^2]*(x*y +
              Sqrt[(-1 + x^2)*(-1 + y^2)]), (-1 + x^2)*y +
           x*Sqrt[(-1 + x^2)*(-1 + y^2)]]}}



Bob Hanlon




On Sun, Apr 27, 2014 at 9:44 PM, Narasimham <mathma18 at gmail.com> wrote:

> Solve[ {x == Cos[u], y == Cos[u + v] }, {u, v} ]
>
> Its closed/analytic solution is not possible, even numerically.
>
> The known solutions are ellipses from sine waves with a phase difference,
> having x^2, x y and y^2 terms, as also sketched in Lissajous curves:
>
> ParametricPlot[{Cos[u], Cos[u + v]}, {u, -Pi, Pi}, {v, -Pi, Pi}]
>
> Can there be a work around?
>
> Narasimham
>
>




  • Prev by Date: Suzhou, China
  • Next by Date: Re: Inverse function solution
  • Previous by thread: Inverse function solution
  • Next by thread: Re: Inverse function solution