Re: solving a trigonometric equation for a variable

Cap <[email protected]> writes:

> Hello there!
>
> Well look, I'm a total axiom newbie and don't have much clue about math either. I really tried to solve this on my own, spent half a day to find what I need in the axiom documentation, but it's huge and I barely understand anything of it. Can you please help me out?
>
> I need to deal with the following equation:
>
> 0.5 * v*v * cos(theta + phi) * cos(theta + phi) + g*l * cos(phi) = g*l
>
> The variables v, theta, g and l are known. I need to calculate a phi
> that satisfies the equation above. So I would like to solve the
> equation for phi so that it starts with phi = ... This way any time I
> get a new set of v, theta, g and l, I can calculate a new phi. How can
> accomplish this using axiom? I tried:

Your command is mostly correct -- instead of 0.5 use 1/2:
>
> solve(0.5*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l, phi)
>
> The answer I get is:
>
>  Cannot find a definition or applicable library operation named solve
>       with argument type(s) 
>                           Equation Expression Float
>                                 Variable phi

This says: there is no command solve that takes a float expression
(i.e., expression involving variables, floats and elementary) and a
variable.

Thus:

(1) -> solve(1/2*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l,phi)

gives you 4 solutions, one being 2*atan(%phi0).

   (1)
   [phi= 2atan(%phi0) - theta, phi= 2atan(%phi1) - theta,

-- skipped --
                                    Type: List(Equation(Expression(Integer)))

You get the value of %phi0 as follows:

(4) -> definingPolynomial %phi0

   (4)
              4         2      2            2             theta 2
       ((%phi0  - 2%phi0  + 1)v  + (- 4%phi0  - 4)g l)tan(-----)
                                                            2
     + 
              3                  theta          4         2      2
       (8%phi0  + 8%phi0)g l tan(-----) + (%phi0  - 2%phi0  + 1)v
                                   2
     + 
                4         2
       (- 4%phi0  - 4%phi0 )g l
  /
      2    theta 2    2
     v tan(-----)  + v  - 4g l
             2
                                                    Type: Expression(Integer)

Not really nice, but more I was hoping for...

Hope that helps,

Martin