Make all fraction bars have the same lenght in a set of equations

Question

I am a begginer at LaTex
Bassically i want every fraction bar to have the same lenght as the natural lenght of the biggest one
I dont know if it would be better to use other command instead of equations, maybe an array or something like that
begin{equation}
begin{aligned}
        dot { { x }_{ 1 } } = & enskip { x }_{ 2 }
            dot { { x }_{ 2 } } = & enskip frac { beta gamma {{ x }_{ 2 }}^{ 2 }(sin ^{ 2 }{ { x }_{ 3 } } -1)sin { { x }_{ 3 } }  }{ varphi beta -gamma ^{ 2 }+(beta ^{ 2 }+gamma ^{ 2 })sin ^{ 2 }{ alpha  }  }  
        &-frac { 2beta ^{ 2 }{ x }_{ 2 }{ x }_{ 4 }cos { { x }_{ 3 } } sin { { x }_{ 3 } }  }{ varphi beta -gamma ^{ 2 }+(beta ^{ 2 }+gamma ^{ 2 })sin ^{ 2 }{alpha}  }  
             &+frac { beta gamma {dot { {{ x }_{ 3 }}}^{ 2 }sin { { x }_{ 3 } } }-gamma delta cos { { x }_{ 3 } }sin { { x }_{ 3 } }+beta {tau}_{theta} }{ varphi beta -gamma ^{ 2 }+(beta ^{ 2 }+gamma ^{ 2 } sin ^{ 2 }{alpha}  }
end{aligned}   
end{equation}

egreg · Accepted Answer

This is how I'd type in the diagram. Note dot{x}_1, so the dot is not at a weird position. I also removed several useless and difficult to parse braces. Also enskip is not the right space to use. It should be mskipthickmuskip, but it's easier to use &= instead.
documentclass{article}
usepackage{amsmath}

begin{document}

begin{equation}
begin{aligned}
dot{x}_{1} &= x_{2} 
dot{x}_{2}
  &= frac{betagamma {x_{2}}^{2}(sin^{2} x_{3} - 1)sin x_{3}}
          {varphibeta - gamma^{2}+(beta^{2} + gamma^{2})sin^{2}alpha} 
  &qquad
   -frac{2beta^{2} x_{2}x_{4}cos x_{3} sin x_{3}}
         {varphibeta - gamma^{2} + (beta^{2} + gamma^{2})sin^{2}alpha} 
  &qquad
   +frac{betagamma{{}dot{x}_{3}}^{2}sin x_{3} - gammadeltacos x_{3}sin x_{3}
          +betatau_{theta}}
         {varphibeta-gamma^{2}+(beta^{2}+gamma^{2})sin^{2}alpha}
end{aligned}
end{equation}

end{document}

Now, if you want to equalize the last two fractions, you can use eqparbox.
The first argument to eqfrac is a label (here A) unique to the fractions you want to equalize. Note that this might require multiple LaTeX runs, but you get a warning if a rerun is needed.
documentclass{article}
usepackage{amsmath}
usepackage{eqparbox}

newcommand{eqfrac}[3]{%
% #1 = label for the objects to equalize
% #2 = numerator
% #3 = denominator
  frac{eqmakebox[#1][c]{$#2$}}{eqmakebox[#1][c]{$#3$}}%
}

begin{document}

begin{equation}
begin{aligned}
dot{x}_{1} &= x_{2} 
dot{x}_{2}
  &= frac{betagamma {x_{2}}^{2}(sin^{2} x_{3} - 1)sin x_{3}}
          {varphibeta - gamma^{2}+(beta^{2} + gamma^{2})sin^{2}alpha} 
  &qquad
   -eqfrac{A}{2beta^{2} x_{2}x_{4}cos x_{3} sin x_{3}}
              {varphibeta - gamma^{2} + (beta^{2} + gamma^{2})sin^{2}alpha} 
  &qquad
   +eqfrac{A}{betagamma{{}dot{x}_{3}}^{2}sin x_{3} - gammadeltacos x_{3}sin x_{3}
                 +betatau_{theta}}
              {varphibeta-gamma^{2}+(beta^{2}+gamma^{2})sin^{2}alpha}
end{aligned}   
end{equation}

end{document}

Do you really see an improvement? I don't, but it's just my opinion.

wipet · Answer

If you know what numerator or denominator is widest then you can measure it right before printing the equation using setbox TeX primitive. Then you can do a construction:
{ hbox to<measured width>{$numerator$} over denominator }

for creating a fractions with wider fraction rule. It looks like:
newboxtmpbox
defcentereq#1{hbox towdtmpbox{hss$#1$hss}}

$$
setboxtmpbox=hbox{$beta gamma dot  x_3^2 sin x_3 
                     - gamma delta cos x_3 sin x_3 + beta tau_theta $} 
eqalign{
  dot x_1  &= x_2 cr
  dot x_2  &= { beta gamma x_2^2 (sin^2 x_3 - 1) sin x_3 over 
                 varphi beta - gamma^2 + (beta^2 + gamma^2) sin^2 alpha } cr 
            &quad - { centereq{2beta^2 x_2  x_4 cos x_3 sin x_3} over
                       varphi beta - gamma^2 + (beta^2 + gamma^2) sin ^2alpha  } cr
            &quad + { copytmpbox over 
                       varphi beta - gamma ^2 + (beta^2 + gamma^2 sin^2 alpha  }
}
$$

in plain TeX. But you are using LaTeX, so put
newboxtmpbox 
defcentereq#1{hbox towdtmpbox{hss$#1$hss}}

before begin{document} and the code fragment for your equation looks like:
setboxtmpbox=hbox{$beta gamma dot  x_3^2 sin x_3 
                     - gamma delta cos x_3 sin x_3 + beta tau_theta $} 
begin{equation}
begin{aligned}
  dot x_1  &= x_2 cr
  dot x_2  &= { beta gamma x_2^2 (sin^2 x_3 - 1) sin x_3 over 
                 varphi beta - gamma^2 + (beta^2 + gamma^2) sin^2 alpha }  
            &quad - { centereq{2beta^2 x_2  x_4 cos x_3 sin x_3} over
                       varphi beta - gamma^2 + (beta^2 + gamma^2) sin ^2alpha  } 
            &quad + { copytmpbox over 
                       varphi beta - gamma ^2 + (beta^2 + gamma^2 sin^2 alpha  }
end{aligned}
end{equation}

Make all fraction bars have the same lenght in a set of equations

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