FourVelocity.m now uses functions from OrbitalFrequencies.m #50

Kernel/FourVelocity.m

@@ -9,7 +9,8 @@
 
 
 BeginPackage["KerrGeodesics`FourVelocity`",
-	{"KerrGeodesics`ConstantsOfMotion`"}];
+	{"KerrGeodesics`ConstantsOfMotion`",
+	"KerrGeodesics`OrbitalFrequencies`"}];
 
 KerrGeoFourVelocity::usage = "KerrGeoVelocity[a,p,e,x] returns the four-velocity components as parametrized functions.";
 
@@ -27,7 +28,7 @@
 (*Schwarzschild*)
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Circular, Equatorial*)
 
 
@@ -66,45 +67,31 @@
 ] 
 
 
-(* ::Subsection:: *)
-(*Eccentric*)
-
-
 (* ::Section:: *)
 (*Kerr*)
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Generic (Mino)*)
 
 
-(* ::Text:: *)
-(*FixMe: Circular Equatorial Retrograde orbits don't normalize to -1*)
-
-
 KerrGeoVelocityMino[a_,p_,e_,x_,initPhases_,index_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z, 
 qr, qz, \[Lambda]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], utContra,urContra,u\[Theta]Contra,uzContra,u\[Phi]Contra, utCo, urCo, u\[Theta]Co, u\[Phi]Co},
 
 (*Constants of Motion*)
 {En,L,Q}= {"\[ScriptCapitalE]","\[ScriptCapitalL]","\[ScriptCapitalQ]"}/.KerrGeoConstantsOfMotion[a,p,e,x];
 
-(*Roots*)
-r1 = p/(1-e);
-r2 = p/(1+e);
-zm = Sqrt[1-x^2];
+{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x];
 
-(*Other Roots*)
-r3 = 1/(1-En^2) - (r1 + r2)/2 + Sqrt[(-(1/(1-En^2)) + (r1 + r2)/2 )^2 - (a^2 Q)/(r1 r2 (1 - En^2))];
-r4  =  (a^2  Q)/(r1 r2 r3 (1-En^2));
+{zp,zm}= KerrGeodesics`OrbitalFrequencies`Private`KerrGeoPolarRoots[a, p, e, x];
 
-zp = Sqrt[a^2 (1 - En^2) + (L^2)/(1 - zm^2) ]; 
 kr = ((r1-r2)(r3-r4))/((r1-r3)(r2-r4));
 
 kz = a^2 (1-En^2) zm^2/zp^2;
 
 (*Frequencies*)
-\[CapitalUpsilon]r = \[Pi]/(2 EllipticK[kr]) Sqrt[(1 - En^2)(r1 - r3)(r2 - r4)]; 
-\[CapitalUpsilon]z = (\[Pi] zp)/(2EllipticK[kz] ); 
+\[CapitalUpsilon]r = KerrGeodesics`OrbitalFrequencies`Private`KerrGeoMinoFrequencyr[a,p,e,x,{En,L,Q},{r1,r2,r3,r4}]; 
+\[CapitalUpsilon]z = KerrGeodesics`OrbitalFrequencies`Private`KerrGeoMinoFrequency\[Theta][a,p,e,x,{En,L,Q},{zp,zm}];
 
 (*Action Angle Phases*)
 { qr0, qz0} = {initPhases[[1]], initPhases[[2]]};
@@ -153,7 +140,7 @@
 (*Equatorial (Darwin)*)
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*Circular Case*)
 
 
@@ -176,7 +163,7 @@
 ]
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*Eccentric Case*)
 
 
@@ -187,16 +174,12 @@
 {En,L,Q}= {"\[ScriptCapitalE]","\[ScriptCapitalL]","\[ScriptCapitalQ]"}/.KerrGeoConstantsOfMotion[a,p,e,x];
 
 (*Roots*)
-r1 = p/(1-e);
-r2 = p/(1+e);
+{r1,r2,r3,r4}=KerrGeodesics`OrbitalFrequencies`Private`KerrGeoRadialRoots[a, p, e, x];
 
-(*Other Roots*)
-r3 = 1/(1-En^2) - (r1 + r2)/2 + Sqrt[(-(1/(1-En^2)) + (r1 + r2)/2 )^2 - (a^2 Q)/(r1 r2 (1 - En^2))];
-r4  =  (a^2  Q)/(r1 r2 r3 (1-En^2));
 kr = ((r1-r2)(r3-r4))/((r1-r3)(r2-r4));
 
 (*Frequencies*)
-\[CapitalUpsilon]r = \[Pi]/(2 EllipticK[kr]) Sqrt[(1 - En^2)(r1 - r3)(r2 - r4)]; 
+\[CapitalUpsilon]r = KerrGeodesics`OrbitalFrequencies`Private`KerrGeoMinoFrequencyr[a,p,e,x,{En,L,Q},{r1,r2,r3,r4}]; 
 
 (*Initial Phase*)
 \[Chi]0 = initPhases[[1]];
@@ -232,7 +215,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*KerrGeoFourVelocity Wrapper*)
 
 

Kernel/KerrGeoOrbit.m

@@ -19,7 +19,7 @@
 KerrGeoOrbitFunction::usage = "KerrGeoOrbitFunction[a,p,e,x,assoc] an object for storing the trajectory and orbital parameters in the assoc Association.";
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Error messages*)
 
 
@@ -36,7 +36,7 @@
 Begin["`Private`"];
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Error messages*)
 
 
@@ -515,7 +515,7 @@
 
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Generic (Mino)*)
 
 
@@ -723,7 +723,7 @@
 
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Generic (Fast Spec - Mino)*)
 
 
@@ -1231,7 +1231,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*KerrGeoOrbit and KerrGeoOrbitFuction*)
 
 

Kernel/OrbitalFrequencies.m

@@ -16,7 +16,7 @@
 Begin["`Private`"];
 
 
-(* ::Section::Closed:: *)
+(* ::Section:: *)
 (*Roots of the radial and polar equations*)
 
 
@@ -121,11 +121,11 @@
 KerrGeoProperFrequencyFactor[a_?PossibleZeroQ ,p_,e_,x_]:=(p^2 ((1+e) (28+4 e^2+(-12+p) p)-((1+e) (-4+p) (-6+2 e+p) EllipticE[(4 e)/(-6+2 e+p)]+2 (6+2 e-p) (3+e^2-p) EllipticPi[(2 e (-4+p))/((1+e) (-6+2 e+p)),(4 e)/(-6+2 e+p)])/EllipticK[(4 e)/(-6+2 e+p)]))/(2 (-1+e) (1+e)^2 (-4+p)^2)
 
 
-(* ::Subsection::Closed:: *)
+(* ::Subsection:: *)
 (*Kerr*)
 
 
-(* ::Subsubsection::Closed:: *)
+(* ::Subsubsection:: *)
 (*KerrGeoMinoFrequencyr*)
 
 
@@ -147,7 +147,7 @@
 
 
 
-(* ::Subsubsection::Closed:: *)
+(* ::Subsubsection:: *)
 (*KerrGeoMinoFrequency\[Theta]*)
 
 

Kernel/SpecialOrbits.m

@@ -16,7 +16,7 @@
 	{"KerrGeodesics`ConstantsOfMotion`"}];
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Usage messages*)
 
 
@@ -81,7 +81,7 @@
 ];
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Photon Sphere*)
 
 
@@ -254,7 +254,7 @@
 KerrGeoISSO[a_,x_]:=KerrGeoSeparatrix[a,0,x]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Bound Orbit Q*)
 
 
@@ -264,7 +264,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Scatter Orbit Q*)
 
 
@@ -275,7 +275,7 @@
 KerrGeoScatterOrbitQ[a_?NumericQ, p_?NumericQ, e_?NumericQ, x_?NumericQ] := If[p >= KerrGeoSeparatrix[a,e,x] && e >= 1, True, False]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Plunge Orbit Q*)
 
 
@@ -287,7 +287,7 @@
 	If[KerrGeoBoundOrbitQ[0,p,e,1] == KerrGeoScatterOrbitQ[0,p,e,1] == False, True, False]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*OnSeparatrixQ*)
 
 
@@ -356,7 +356,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Resonances*)