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
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.
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}
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}
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@?}