Using Phasors in Mathematica (adding Cos[])

Questions
,
1

Hi,
I am calculating both the amplitude and phase angle in electrical circuits that contain capacitors and inductors. Therefore I need to sum Cos[]'s in Mathematica in which I am having difficulty. Additionally I tried to use Phasor Notation to perform the summations without any success. The calculations are easily performed using my TI-89 calculator, but cannot duplicate the calculations using Mathematica: however I would much prefer to use Mathematica. Please review the attached Mathematica file for details and give me your thoughts. My version of Mathematica is 9.0.1.0.

Thanks,

Mitch Sandlin

2

You can replace the Cos[x] by a complex exponential E^(I x). All operations are easier with the exponentials. At the end, take the real part of the result.

3

In[1]:= eq1 =
a1 Exp[I ( [Omega] t + [Phi]1)] + a2 Exp[ I ([Omega] t + [Phi]2)]

Out[1]= a1 E^(I (\[Phi]1 + t \[Omega])) + 
 a2 E^(I (\[Phi]2 + t \[Omega]))

In[2]:= eq2 = CoefficientList[eq1, Exp[I \[Omega] t]]

Out[2]= {0, a1 E^(I \[Phi]1) + a2 E^(I \[Phi]2)}

In[3]:= eq3 = 
 eq2[[2]] /. { a1 -> 5, 
   a2 -> 10, \[Phi]1 -> 36.87 Degree, \[Phi]2 -> - 53.13 Degree}

Out[3]= 10. - 4.99998 I

In[4]:= {1., 1./Degree} * 
 CoordinateTransform["Cartesian" -> "Polar", ReIm[eq3]]

Out[4]= {11.1803, -26.5649}
4

This is one way of many:

phasorAdd°[{rA_, ?A_}, {rB_, ?B_}] :=
  MapAt[
    #/°&,
    ToPolarCoordinates[
      FromPolarCoordinates[{rA, ?A °}] + 
      FromPolarCoordinates[{rB, ?B °}]
   	],
  	2
  ]

phasorAdd°[{5, 36.87}, {10, -53.13}]
{11.1803, -26.5649}
5

Now realized that Mitchell said he has MMA 9. To/FromPolarCoordinates are new in 10. So:

toPolarCoordinates[vect : {x_, y_}] := {Norm@vect, ArcTan[x, y]}

fromPolarCoordinates[{r_, ?_}] := r {Cos@?, Sin@?}