Simple matrix library + formula for precession.

5 files changed, 111 insertions, 439 deletions

diff --git a/org/madore/ephem/Comput.java b/org/madore/ephem/Comput.java
index dee77f0..214d5e8 100644
--- a/org/madore/ephem/Comput.java
+++ b/org/madore/ephem/Comput.java
@@ -6,6 +6,9 @@ import java.util.Arrays;
 
 public final class Comput {
 
+    public static final double degree = Math.PI/180;
+    public static final double arcsecond = degree/3600;
+
     public static final double ipow(double x, int n) {
 	if ( n == 0 )
 	    return 1;
@@ -127,7 +130,7 @@ public final class Comput {
 	public Polynomial(Double[] c) {
 	    this(Arrays.asList(c));
 	}
-	public Polynomial(double[] c) {
+	public Polynomial(double... c) {
 	    this(boxDoubleArray(c));
 	}
 	public double v(double t) {
diff --git a/org/madore/ephem/Frames.java b/org/madore/ephem/Frames.java
new file mode 100644
index 0000000..e85412c
--- /dev/null
+++ b/org/madore/ephem/Frames.java
@@ -0,0 +1,85 @@
+package org.madore.ephem;
+
+public final class Frames {
+
+    private static double[] unboxDoubleArray(Double[] c) {
+	double[] unboxed = new double[c.length];
+	for ( int i=0 ; i<unboxed.length ; i++ )
+	    unboxed[i] = c[i];
+	return unboxed;
+    }
+
+    public static final class Vector {
+	double[] crd;
+	public Vector(double... crd) {
+	    if ( crd.length != 3 )
+		throw new IllegalArgumentException("Vector constructor expects 3 coordinates");
+	    this.crd = crd;
+	}
+	public Vector(Double... crd) {
+	    this(unboxDoubleArray(crd));
+	}
+	public double dotprod(Vector v) {
+	    double res = 0;
+	    for ( int i=0 ; i<3 ; i++ )
+		res += crd[i]*v.crd[i];
+	    return res;
+	}
+	public double sqnorm() {
+	    double res = 0;
+	    for ( int i=0 ; i<3 ; i++ )
+		res += crd[i]*crd[i];
+	    return res;
+	}
+    }
+
+    public static final class RotationMatrix {
+	double[][] mat;
+	public RotationMatrix(double[][] mat) {
+	    if ( mat.length != 3 )
+		throw new IllegalArgumentException("RotationMatrix constructor expects 3 lines");
+	    for ( int i=0 ; i<3 ; i++ )
+		if ( mat[i].length != 3 )
+		    throw new IllegalArgumentException("RotationMatrix constructor expects 3 columns");
+	    this.mat = mat;
+	}
+	private static double[][] matOfVectors(Vector[] vecs) {
+	    double[][] mat = new double[vecs.length][];
+	    for ( int i=0 ; i<mat.length ; i++ )
+		mat[i] = vecs[i].crd;
+	    return mat;
+	}
+	public RotationMatrix(Vector... vecs) {
+	    this(matOfVectors(vecs));
+	}
+	public Vector apply(double[] v) {
+	    double out[] = new double[3];
+	    for ( int i=0 ; i<3 ; i++ )
+		for ( int j=0 ; j<3 ; j++ )
+		    out[i] += v[j]*mat[j][i];
+	    return new Vector(out);
+	}
+	public Vector apply(Vector v) {
+	    return apply(v.crd);
+	}
+	public RotationMatrix apply(RotationMatrix mv) {
+	    return new RotationMatrix(this.apply(mv.mat[0]), this.apply(mv.mat[1]), this.apply(mv.mat[2]));
+	}
+	public static RotationMatrix rotx(double theta) {
+	    return new RotationMatrix(new Vector(1, 0, 0),
+				      new Vector(0, Math.cos(theta), -Math.sin(theta)),
+				      new Vector(0, Math.sin(theta), Math.cos(theta)));
+	}
+	public static RotationMatrix roty(double theta) {
+	    return new RotationMatrix(new Vector(Math.cos(theta), 0, Math.sin(theta)),
+				      new Vector(0, 1, 0),
+				      new Vector(-Math.sin(theta), 0, Math.cos(theta)));
+	}
+	public static RotationMatrix rotz(double theta) {
+	    return new RotationMatrix(new Vector(Math.cos(theta), -Math.sin(theta), 0),
+				      new Vector(Math.sin(theta), Math.cos(theta), 0),
+				      new Vector(0, 0, 1));
+	}
+    }
+
+}
diff --git a/org/madore/ephem/Precession.java b/org/madore/ephem/Precession.java
new file mode 100644
index 0000000..5ac3a03
--- /dev/null
+++ b/org/madore/ephem/Precession.java
@@ -0,0 +1,22 @@
+package org.madore.ephem;
+
+public final class Precession {
+
+    // The following angles are in arcseconds, argument is in Julian centuries since J2000.
+    public static final double epsilon = 84381.406;
+    public static Comput.Polynomial psi
+	= new Comput.Polynomial(0, 5038.481507, -1.0790069, -0.00114045, 0.000132851, -0.0000000951); 
+    public static Comput.Polynomial omega
+	= new Comput.Polynomial(epsilon, -0.025754, 0.0512623, -0.00772503, -0.000000467, 0.0000003337);
+    public static Comput.Polynomial chi
+	= new Comput.Polynomial(0, 10.556403, -2.3814292, -0.00121197, 0.000170663, -0.0000000560);
+
+    public static Frames.RotationMatrix matrix(double t) {
+	Frames.RotationMatrix mat1 = Frames.RotationMatrix.rotx(epsilon*Comput.arcsecond);
+	Frames.RotationMatrix mat2 = Frames.RotationMatrix.rotz(-psi.v(t)*Comput.arcsecond).apply(mat1);
+	Frames.RotationMatrix mat3 = Frames.RotationMatrix.rotx(-omega.v(t)*Comput.arcsecond).apply(mat2);
+	Frames.RotationMatrix mat4 = Frames.RotationMatrix.rotz(chi.v(t)*Comput.arcsecond).apply(mat3);
+	return mat4;
+    }
+
+}
diff --git a/org/madore/ephem/Smart97.java b/org/madore/ephem/Smart97.java
deleted file mode 100644
index 3fa2b80..0000000
--- a/org/madore/ephem/Smart97.java
+++ /dev/null
@@ -1,46 +0,0 @@
-package org.madore.ephem;
-
-import java.util.List;
-import java.util.ArrayList;
-import java.util.EnumMap;
-import java.io.InputStream;
-import java.io.InputStreamReader;
-import java.io.BufferedReader;
-
-public final class Smart97 {
-
-    public static enum Variable {
-	CHI("chi"), P("p"), EPSILON("epsilon"),
-	PHI("phi"), OMEGA("omega"), SIDTIME("sidtime");
-	final String name;
-	Variable(String name) { this.name = name; }
-    }
-
-    private static EnumMap<Variable, Comput.SumPoissonTerms> data = new EnumMap<Variable, Comput.SumPoissonTerms>(Variable.class);
-
-    public static Comput.SumPoissonTerms getFunc(Variable v) {
-	if ( ! data.containsKey(v) ) {
-	    List<Comput.PoissonTerm> series = new ArrayList<Comput.PoissonTerm>();
-	    try {
-		InputStream str = Smart97.class.getResourceAsStream("smart97-simp.dat");
-		BufferedReader in = new BufferedReader(new InputStreamReader(str, "utf-8"));
-		String s;
-		while ( ( s = in.readLine() ) != null ) {
-		    String[] fields = s.split("\t");
-		    if ( ! fields[0].equals("orient") || ! fields[1].equals(v.name) )
-			continue;
-		    int deg = Integer.parseInt(fields[2]);
-		    double c = Double.parseDouble(fields[3]);
-		    double phi = Double.parseDouble(fields[4]);
-		    double om = Double.parseDouble(fields[5]);
-		    series.add(Comput.PoissonTerm.cphi(deg, c, phi, om));
-		}
-	    } catch ( Exception e ) {
-		throw new RuntimeException(e);
-	    }
-	    data.put(v, new Comput.SumPoissonTerms(series));
-	}
-	return data.get(v);
-    }
-
-}
diff --git a/org/madore/ephem/smart97-simp.dat b/org/madore/ephem/smart97-simp.dat
deleted file mode 100644
index 1431272..0000000
--- a/org/madore/ephem/smart97-simp.dat
+++ /dev/null
@@ -1,392 +0,0 @@
-orient	chi	1	105576857.99519999325	0.00000000000	0.00000000000
-orient	chi	1	99190.44310000000	0.50156174030	-337.57047081000
-orient	chi	1	7325.97150000000	1.84631616800	12566.63930559000
-orient	chi	1	1268.67470000000	5.96146554720	167994.18220195000
-orient	chi	1	1202.48390000000	5.84620520680	-675.14094162000
-orient	chi	2	-238245949.46639999747	0.00000000000	0.00000000000
-orient	chi	2	24670.38870000000	2.09788180320	-337.57047081000
-orient	chi	3	-1214073.17859999998	0.00000000000	0.00000000000
-orient	chi	4	1704654.16800000006	0.00000000000	0.00000000000
-orient	p	0	17280776.38599999994	3.75320979740	-337.57047081000
-orient	p	0	1278912.06300000008	5.07720039400	12566.63930559000
-orient	p	0	221506.92410000000	2.90831422500	167994.18220195000
-orient	p	0	209035.06390000001	2.79409290210	-675.14094162000
-orient	p	0	106734.73890000000	4.58200520460	6283.31965280000
-orient	p	0	67768.13550000000	0.78476596240	83286.91424771000
-orient	p	0	49960.82990000000	5.03438172580	18849.95895839000
-orient	p	0	37854.06170000000	0.72584406630	168331.75267275999
-orient	p	0	29581.03730000000	5.26386898410	251281.09644967000
-orient	p	0	14958.08080000000	0.18740069320	72140.62864865000
-orient	p	0	12504.60540000000	6.03706095620	12904.20977640000
-orient	p	0	11925.69320000000	3.69407469280	84707.26795424000
-orient	p	0	6109.40480000000	2.96715973950	82949.34377691000
-orient	p	0	6051.00140000000	2.54358638440	155427.54289636001
-orient	p	0	5845.58840000000	4.66651072760	240134.81085060001
-orient	p	0	5432.57610000000	1.39768334310	-83624.48471852001
-orient	p	0	5094.34690000000	3.08138459550	251618.66692046999
-orient	p	0	4510.37440000000	5.43934771210	1757.92417733000
-orient	p	0	4484.91920000000	0.97343137130	-11146.28559907000
-orient	p	0	3811.93660000000	0.73887625020	323421.72509830998
-orient	p	0	3071.73070000000	1.33623855990	334568.01069738000
-orient	p	0	2788.42160000000	3.14037502650	166573.82849543000
-orient	p	0	2765.67690000000	4.29119037780	95853.55355329999
-orient	p	0	2469.03320000000	1.68504055130	168669.32314357001
-orient	p	0	2056.90180000000	5.57025854000	-13241.78024721000
-orient	p	0	1980.06710000000	1.51174230870	85044.83842504000
-orient	p	0	1527.86160000000	4.99262841880	25133.27861118000
-orient	p	0	1483.45740000000	3.70953104500	5945.74918199000
-orient	p	0	1467.00130000000	2.36982941440	71803.05817783999
-orient	p	0	1427.53410000000	3.64815057260	-6620.89012360000
-orient	p	0	1207.19300000000	1.99497980330	-72478.19911945000
-orient	p	0	1111.91860000000	0.11548655770	2095.49464814000
-orient	p	0	1005.72800000000	2.48404815340	240472.38132141001
-orient	p	0	842.04200000000	5.59856892830	-7.84495195000
-orient	p	0	766.30740000000	3.09443076280	406708.63934603002
-orient	p	0	736.56880000000	6.00679363830	174277.50185475001
-orient	p	0	700.15720000000	6.05258998080	-65857.30899585001
-orient	p	0	660.64550000000	4.83958631960	323759.29556911997
-orient	p	0	637.19420000000	2.99537674760	161710.86254916000
-orient	p	0	632.02190000000	4.90196450170	238714.45714407999
-orient	p	0	627.80930000000	0.36392533770	179140.46780101999
-orient	p	0	614.45800000000	1.58379563520	155089.97242554999
-orient	p	0	562.47070000000	2.10906067610	96191.12402411000
-orient	p	0	532.83290000000	5.43692547570	334905.58116818999
-orient	p	0	523.00570000000	3.15587139240	-11483.85606988000
-orient	p	0	458.77810000000	5.92210348110	-155765.11336717001
-orient	p	0	449.78910000000	5.45481956240	-77003.59459492000
-orient	p	0	414.52360000000	3.69690940370	-149144.22324357001
-orient	p	0	402.87760000000	0.48609998210	77713.77144818001
-orient	p	0	398.39310000000	1.20887926740	10808.71512826000
-orient	p	0	386.58290000000	2.47103739930	85382.40889585001
-orient	p	0	347.05880000000	5.99379835980	19187.52942919000
-orient	p	0	319.16350000000	4.04065949090	251956.23739128001
-orient	p	0	316.57010000000	3.87336395710	89570.23390050999
-orient	p	0	289.57980000000	3.69179448000	417854.92494509002
-orient	p	0	283.31470000000	4.51324995520	1420.35370652000
-orient	p	0	274.17680000000	4.71307683910	233851.49119780000
-orient	p	0	273.40410000000	5.32263686090	244997.77679686999
-orient	p	0	260.47770000000	0.78370966930	317138.40544552001
-orient	p	0	255.98080000000	1.27205989590	-5573.14279953000
-orient	p	0	243.58530000000	2.07915365330	257564.41610246000
-orient	p	0	234.54850000000	1.13225271640	710.17685326000
-orient	p	0	212.99830000000	5.32267627410	166236.25802462001
-orient	p	0	212.38380000000	5.32524118010	-166911.39896624000
-orient	p	1	50306898827.43599700928	0.00000000000	0.00000000000
-orient	p	1	174568.49830000001	3.76205616090	-337.57047081000
-orient	p	1	43199.35620000000	3.10358022600	6283.31965280000
-orient	p	1	15046.59260000000	3.38277711640	18849.95895839000
-orient	p	2	111293456.43260000646	0.00000000000	0.00000000000
-orient	p	2	62639.37290000000	5.31160575050	-337.57047081000
-orient	p	3	77665.76700000001	0.00000000000	0.00000000000
-orient	p	4	-235686.42559999999	0.00000000000	0.00000000000
-orient	epsilon	0	84381409000.00000000000	0.00000000000	0.00000000000
-orient	epsilon	0	9227886.93139999919	2.18244238680	-337.57047081000
-orient	epsilon	0	553345.22290000005	3.50693920000	12566.63930559000
-orient	epsilon	0	94918.48860000000	1.33751928830	167994.18220195000
-orient	epsilon	0	90339.74230000000	1.22332373290	-675.14094162000
-orient	epsilon	0	21620.35430000000	3.46381106990	18849.95895839000
-orient	epsilon	0	19412.99430000000	5.43824278270	168331.75267275999
-orient	epsilon	0	12609.76530000000	3.69307429040	251281.09644967000
-orient	epsilon	0	9114.58470000000	0.41502644410	6283.31965280000
-orient	epsilon	0	6634.66450000000	4.46590291020	12904.20977640000
-orient	epsilon	0	5136.13240000000	2.12354696720	84707.26795424000
-orient	epsilon	0	3194.45680000000	1.39640779680	82949.34377691000
-orient	epsilon	0	2967.10060000000	6.11009115720	-83624.48471852001
-orient	epsilon	0	2566.06700000000	1.51059992300	251618.66692046999
-orient	epsilon	0	2493.56490000000	3.09571196410	240134.81085060001
-orient	epsilon	0	2404.90260000000	3.86886644700	1757.92417733000
-orient	epsilon	0	1618.04280000000	5.45126660760	323421.72509830998
-orient	epsilon	0	1303.01790000000	6.04862928640	334568.01069738000
-orient	epsilon	0	1189.62710000000	2.72090202130	95853.55355329999
-orient	epsilon	0	1034.48780000000	6.22443030720	85044.83842504000
-orient	epsilon	0	972.74300000000	5.49686803840	83286.91424771000
-orient	epsilon	0	790.78810000000	2.13916245590	5945.74918199000
-orient	epsilon	0	769.17620000000	0.79904961800	71803.05817783999
-orient	epsilon	0	660.08070000000	3.42129818670	25133.27861118000
-orient	epsilon	0	657.15570000000	0.42428312500	-72478.19911945000
-orient	epsilon	0	507.77900000000	0.91325542640	240472.38132141001
-orient	epsilon	0	497.79640000000	1.04294904930	-7.84495195000
-orient	epsilon	0	327.94350000000	3.26879936630	323759.29556911997
-orient	epsilon	0	323.76810000000	1.52363622210	406708.63934603002
-orient	epsilon	0	316.05030000000	0.01299138640	155089.97242554999
-orient	epsilon	0	315.49690000000	4.43599205700	174277.50185475001
-orient	epsilon	0	312.80360000000	2.59239314220	-6620.89012360000
-orient	epsilon	0	296.04220000000	1.38324581150	161710.86254916000
-orient	epsilon	0	293.04410000000	0.53863682940	96191.12402411000
-orient	epsilon	0	280.06830000000	1.58509921470	-11483.85606988000
-orient	epsilon	0	268.74990000000	5.07646207800	179140.46780101999
-orient	epsilon	0	263.92190000000	3.86614219990	334905.58116818999
-orient	epsilon	0	255.34220000000	4.35243168530	-155765.11336717001
-orient	epsilon	0	212.03650000000	5.92146364290	10808.71512826000
-orient	epsilon	1	-468360500.64600002766	0.00000000000	0.00000000000
-orient	epsilon	1	9316.15190000000	2.27862197390	-337.57047081000
-orient	epsilon	1	6517.42420000000	1.79214083150	18849.95895839000
-orient	epsilon	1	2878.63980000000	0.33015300600	12566.63930559000
-orient	epsilon	1	2820.52690000000	2.07132188900	6283.31965280000
-orient	epsilon	2	33422.37490000000	3.75353070530	-337.57047081000
-orient	epsilon	2	-18678.63290000000	0.00000000000	0.00000000000
-orient	epsilon	3	2003221.05249999999	0.00000000000	0.00000000000
-orient	phi	0	1009658226149.36914062500	0.00000000000	0.00000000000
-orient	phi	0	15852155.04250000045	3.75320978930	-337.57047081000
-orient	phi	0	1173383.37370000011	5.07720039550	12566.63930559000
-orient	phi	0	203228.36730000001	2.90831422500	167994.18220195000
-orient	phi	0	191849.88690000001	2.79409288760	-675.14094162000
-orient	phi	0	97927.25060000000	4.58200487770	6283.31965280000
-orient	phi	0	62175.96130000000	0.78476596230	83286.91424771000
-orient	phi	0	45838.29610000000	5.03438161810	18849.95895839000
-orient	phi	0	34728.49520000000	0.72584406690	168331.75267275999
-orient	phi	0	27140.03560000000	5.26386898490	251281.09644967000
-orient	phi	0	13723.74240000000	0.18740069710	72140.62864865000
-orient	phi	0	11483.66190000000	6.03706028040	12904.20977640000
-orient	phi	0	10941.58540000000	3.69407469400	84707.26795424000
-orient	phi	0	5604.67230000000	2.96715973790	82949.34377691000
-orient	phi	0	5551.82510000000	2.54358636180	155427.54289636001
-orient	phi	0	5363.21550000000	4.66651073640	240134.81085060001
-orient	phi	0	4983.69080000000	1.39768334340	-83624.48471852001
-orient	phi	0	4673.71380000000	3.08138459510	251618.66692046999
-orient	phi	0	4138.32840000000	5.43934774160	1757.92417733000
-orient	phi	0	4114.82700000000	0.97343136360	-11146.28559907000
-orient	phi	0	3497.37870000000	0.73887625570	323421.72509830998
-orient	phi	0	2818.25410000000	1.33623857100	334568.01069738000
-orient	phi	0	2558.32340000000	3.14037501070	166573.82849543000
-orient	phi	0	2537.42260000000	4.29119037880	95853.55355329999
-orient	phi	0	2265.60960000000	1.68504052840	168669.32314357001
-orient	phi	0	1887.37520000000	5.57025857470	-13241.78024721000
-orient	phi	0	1816.57210000000	1.51174230290	85044.83842504000
-orient	phi	0	1402.09590000000	4.99273410410	25133.27861118000
-orient	phi	0	1362.06830000000	3.70947033670	5945.74918199000
-orient	phi	0	1345.81570000000	2.36982947630	71803.05817783999
-orient	phi	0	1308.84680000000	3.64799056260	-6620.89012360000
-orient	phi	0	1107.44410000000	1.99497976870	-72478.19911945000
-orient	phi	0	1020.19200000000	0.11548656780	2095.49464814000
-orient	phi	0	922.68640000000	2.48404819000	240472.38132141001
-orient	phi	0	779.04970000000	5.59991530910	-7.84495195000
-orient	phi	0	703.07230000000	3.09443075980	406708.63934603002
-orient	phi	0	675.78910000000	6.00679470100	174277.50185475001
-orient	phi	0	642.38020000000	6.05259017320	-65857.30899585001
-orient	phi	0	606.09710000000	4.83958627950	323759.29556911997
-orient	phi	0	584.61220000000	2.99537894890	161710.86254916000
-orient	phi	0	579.88670000000	4.90196440410	238714.45714407999
-orient	phi	0	576.00160000000	0.36392524640	179140.46780101999
-orient	phi	0	563.80930000000	1.58379568140	155089.97242554999
-orient	phi	0	516.03110000000	2.10906072550	96191.12402411000
-orient	phi	0	488.83780000000	5.43692539050	334905.58116818999
-orient	phi	0	479.80780000000	3.15587172480	-11483.85606988000
-orient	phi	0	420.89080000000	5.92210365350	-155765.11336717001
-orient	phi	0	412.67190000000	5.45481896740	-77003.59459492000
-orient	phi	0	380.32400000000	3.69690927330	-149144.22324357001
-orient	phi	0	369.63250000000	0.48609985310	77713.77144818001
-orient	phi	0	365.47590000000	1.20887930670	10808.71512826000
-orient	phi	0	354.69950000000	2.47103741190	85382.40889585001
-orient	phi	0	318.85230000000	5.99379743800	19187.52942919000
-orient	phi	0	292.86940000000	4.04065959360	251956.23739128001
-orient	phi	0	290.44730000000	3.87336449470	89570.23390050999
-orient	phi	0	265.68390000000	3.69179340690	417854.92494509002
-orient	phi	0	260.01650000000	4.51323974000	1420.35370652000
-orient	phi	0	251.55180000000	4.71307668770	233851.49119780000
-orient	phi	0	250.84270000000	5.32263761850	244997.77679686999
-orient	phi	0	238.98320000000	0.78370859050	317138.40544552001
-orient	phi	0	234.85740000000	1.27205990230	-5573.14279953000
-orient	phi	0	223.48490000000	2.07915316860	257564.41610246000
-orient	phi	0	215.18220000000	1.13223468610	710.17685326000
-orient	phi	1	474660027824506304.00000000000	0.00000000000	0.00000000000
-orient	phi	1	78159.47740000000	3.91137988910	-337.57047081000
-orient	phi	1	39600.31500000000	3.09081155350	6283.31965280000
-orient	phi	1	13801.05610000000	3.36529971930	18849.95895839000
-orient	phi	1	5397.29530000000	1.91297962050	12566.63930559000
-orient	phi	2	-98382922.28079999983	0.00000000000	0.00000000000
-orient	phi	2	32899.45580000000	5.36209651180	-337.57047081000
-orient	phi	3	-1216206.28879999998	0.00000000000	0.00000000000
-orient	phi	4	1408224.68969999999	0.00000000000	0.00000000000
-orient	omega	0	84381409000.00000000000	0.00000000000	0.00000000000
-orient	omega	0	9227886.93160000071	2.18244238680	-337.57047081000
-orient	omega	0	553345.22259999998	3.50693920000	12566.63930559000
-orient	omega	0	94918.48870000000	1.33751928820	167994.18220195000
-orient	omega	0	90339.74219999999	1.22332373280	-675.14094162000
-orient	omega	0	21620.35420000000	3.46381107040	18849.95895839000
-orient	omega	0	19412.99400000000	5.43824278270	168331.75267275999
-orient	omega	0	12609.76520000000	3.69307429020	251281.09644967000
-orient	omega	0	9114.58470000000	0.41502644070	6283.31965280000
-orient	omega	0	6634.66410000000	4.46590291080	12904.20977640000
-orient	omega	0	5136.13230000000	2.12354696720	84707.26795424000
-orient	omega	0	3194.45670000000	1.39640779680	82949.34377691000
-orient	omega	0	2967.10060000000	6.11009115720	-83624.48471852001
-orient	omega	0	2566.06690000000	1.51059992280	251618.66692046999
-orient	omega	0	2493.56470000000	3.09571196180	240134.81085060001
-orient	omega	0	2404.90260000000	3.86886644700	1757.92417733000
-orient	omega	0	1618.04270000000	5.45126660260	323421.72509830998
-orient	omega	0	1303.01770000000	6.04862928640	334568.01069738000
-orient	omega	0	1189.62700000000	2.72090202140	95853.55355329999
-orient	omega	0	1034.48790000000	6.22443030720	85044.83842504000
-orient	omega	0	972.74310000000	5.49686803830	83286.91424771000
-orient	omega	0	790.78790000000	2.13916252750	5945.74918199000
-orient	omega	0	769.17580000000	0.79904961540	71803.05817783999
-orient	omega	0	660.08070000000	3.42129818670	25133.27861118000
-orient	omega	0	657.15580000000	0.42428312500	-72478.19911945000
-orient	omega	0	507.77880000000	0.91325542650	240472.38132141001
-orient	omega	0	497.79640000000	1.04294904930	-7.84495195000
-orient	omega	0	327.94360000000	3.26879936590	323759.29556911997
-orient	omega	0	323.76810000000	1.52363622210	406708.63934603002
-orient	omega	0	316.05030000000	0.01299138670	155089.97242554999
-orient	omega	0	315.49680000000	4.43599205710	174277.50185475001
-orient	omega	0	312.80370000000	2.59239310560	-6620.89012360000
-orient	omega	0	296.04220000000	1.38324585250	161710.86254916000
-orient	omega	0	293.04400000000	0.53863682930	96191.12402411000
-orient	omega	0	280.06770000000	1.58509920750	-11483.85606988000
-orient	omega	0	268.75020000000	5.07646207860	179140.46780101999
-orient	omega	0	263.92210000000	3.86614219950	334905.58116818999
-orient	omega	0	255.34190000000	4.35243168580	-155765.11336717001
-orient	omega	0	212.03640000000	5.92146364260	10808.71512826000
-orient	omega	1	-265001.70850000001	0.00000000000	0.00000000000
-orient	omega	1	10269.74170000000	2.62661855990	-337.57047081000
-orient	omega	1	6507.30360000000	1.79198364400	18849.95895839000
-orient	omega	1	2899.36610000000	0.24027679520	12566.63930559000
-orient	omega	1	2803.00860000000	2.07589567810	6283.31965280000
-orient	omega	2	5129588.35670000035	0.00000000000	0.00000000000
-orient	omega	2	25499.80480000000	3.75369012680	-337.57047081000
-orient	omega	3	-7731881.22209999990	0.00000000000	0.00000000000
-orient	psi	0	17280776.38599999994	3.75320979740	-337.57047081000
-orient	psi	0	1278912.06300000008	5.07720039400	12566.63930559000
-orient	psi	0	221506.92410000000	2.90831422500	167994.18220195000
-orient	psi	0	209035.06390000001	2.79409290230	-675.14094162000
-orient	psi	0	106734.73880000001	4.58200520470	6283.31965280000
-orient	psi	0	67768.13550000000	0.78476596220	83286.91424771000
-orient	psi	0	49960.82990000000	5.03438172610	18849.95895839000
-orient	psi	0	37854.06170000000	0.72584406850	168331.75267275999
-orient	psi	0	29581.03740000000	5.26386898480	251281.09644967000
-orient	psi	0	14958.08080000000	0.18740069680	72140.62864865000
-orient	psi	0	12504.60540000000	6.03706096520	12904.20977640000
-orient	psi	0	11925.69320000000	3.69407469410	84707.26795424000
-orient	psi	0	6109.40480000000	2.96715974310	82949.34377691000
-orient	psi	0	6051.00140000000	2.54358637610	155427.54289636001
-orient	psi	0	5845.58840000000	4.66651073600	240134.81085060001
-orient	psi	0	5432.57610000000	1.39768334260	-83624.48471852001
-orient	psi	0	5094.34690000000	3.08138459740	251618.66692046999
-orient	psi	0	4510.37440000000	5.43934771410	1757.92417733000
-orient	psi	0	4484.91920000000	0.97343136340	-11146.28559907000
-orient	psi	0	3811.93660000000	0.73887625500	323421.72509830998
-orient	psi	0	3071.73070000000	1.33623857080	334568.01069738000
-orient	psi	0	2788.42160000000	3.14037501060	166573.82849543000
-orient	psi	0	2765.67690000000	4.29119038570	95853.55355329999
-orient	psi	0	2469.03320000000	1.68504053480	168669.32314357001
-orient	psi	0	2056.90180000000	5.57025854440	-13241.78024721000
-orient	psi	0	1980.06710000000	1.51174229630	85044.83842504000
-orient	psi	0	1527.86160000000	4.99262841820	25133.27861118000
-orient	psi	0	1483.45740000000	3.70953107520	5945.74918199000
-orient	psi	0	1467.00130000000	2.36982947740	71803.05817783999
-orient	psi	0	1427.53410000000	3.64815056670	-6620.89012360000
-orient	psi	0	1207.19300000000	1.99497977650	-72478.19911945000
-orient	psi	0	1111.91860000000	0.11548657370	2095.49464814000
-orient	psi	0	1005.72800000000	2.48404819080	240472.38132141001
-orient	psi	0	842.04200000000	5.59856892780	-7.84495195000
-orient	psi	0	766.30740000000	3.09443075880	406708.63934603002
-orient	psi	0	736.56880000000	6.00679366660	174277.50185475001
-orient	psi	0	700.15720000000	6.05259031850	-65857.30899585001
-orient	psi	0	660.64550000000	4.83958628070	323759.29556911997
-orient	psi	0	637.19420000000	2.99537675750	161710.86254916000
-orient	psi	0	632.02180000000	4.90196451300	238714.45714407999
-orient	psi	0	627.80930000000	0.36392524700	179140.46780101999
-orient	psi	0	614.45790000000	1.58379561910	155089.97242554999
-orient	psi	0	562.47070000000	2.10906071180	96191.12402411000
-orient	psi	0	532.83290000000	5.43692539350	334905.58116818999
-orient	psi	0	523.00570000000	3.15587172260	-11483.85606988000
-orient	psi	0	458.77810000000	5.92210361430	-155765.11336717001
-orient	psi	0	449.78910000000	5.45481991410	-77003.59459492000
-orient	psi	0	414.52360000000	3.69690938280	-149144.22324357001
-orient	psi	0	402.87760000000	0.48609985370	77713.77144818001
-orient	psi	0	398.39310000000	1.20887931570	10808.71512826000
-orient	psi	0	386.58290000000	2.47103741830	85382.40889585001
-orient	psi	0	347.05880000000	5.99379836890	19187.52942919000
-orient	psi	0	319.16350000000	4.04065961180	251956.23739128001
-orient	psi	0	316.57010000000	3.87336389330	89570.23390050999
-orient	psi	0	289.57970000000	3.69179340670	417854.92494509002
-orient	psi	0	283.31470000000	4.51325007280	1420.35370652000
-orient	psi	0	274.17670000000	4.71307652090	233851.49119780000
-orient	psi	0	273.40410000000	5.32263680600	244997.77679686999
-orient	psi	0	260.47760000000	0.78370845900	317138.40544552001
-orient	psi	0	255.98080000000	1.27205988970	-5573.14279953000
-orient	psi	0	243.58530000000	2.07915294800	257564.41610246000
-orient	psi	0	234.54850000000	1.13225290980	710.17685326000
-orient	psi	0	212.99830000000	5.32267653290	166236.25802462001
-orient	psi	0	212.38380000000	5.32524135340	-166911.39896624000
-orient	psi	1	50403763708.80519866943	0.00000000000	0.00000000000
-orient	psi	1	85170.41540000000	3.91141821140	-337.57047081000
-orient	psi	1	43161.88590000000	3.09080993380	6283.31965280000
-orient	psi	1	15042.27050000000	3.36529777090	18849.95895839000
-orient	psi	1	5883.39330000000	1.91298221670	12566.63930559000
-orient	psi	2	-107245239.91429999471	0.00000000000	0.00000000000
-orient	psi	2	35862.24810000000	5.35689626350	-337.57047081000
-orient	psi	2	5216.60830000000	1.20174992780	6283.31965280000
-orient	psi	3	-1144400.22820000001	0.00000000000	0.00000000000
-orient	psi	4	1329512.82609999995	0.00000000000	0.00000000000
-orient	sidtime	0	1009658226149.36914062500	0.00000000000	0.00000000000
-orient	sidtime	0	15852155.04250000045	3.75320978930	-337.57047081000
-orient	sidtime	0	1173383.37370000011	5.07720039550	12566.63930559000
-orient	sidtime	0	203228.36730000001	2.90831422500	167994.18220195000
-orient	sidtime	0	191849.88690000001	2.79409288760	-675.14094162000
-orient	sidtime	0	97927.25060000000	4.58200487770	6283.31965280000
-orient	sidtime	0	62175.96130000000	0.78476596230	83286.91424771000
-orient	sidtime	0	45838.29610000000	5.03438161810	18849.95895839000
-orient	sidtime	0	34728.49520000000	0.72584406690	168331.75267275999
-orient	sidtime	0	27140.03560000000	5.26386898490	251281.09644967000
-orient	sidtime	0	13723.74240000000	0.18740069710	72140.62864865000
-orient	sidtime	0	11483.66190000000	6.03706028040	12904.20977640000
-orient	sidtime	0	10941.58540000000	3.69407469400	84707.26795424000
-orient	sidtime	0	5604.67230000000	2.96715973790	82949.34377691000
-orient	sidtime	0	5551.82510000000	2.54358636180	155427.54289636001
-orient	sidtime	0	5363.21550000000	4.66651073640	240134.81085060001
-orient	sidtime	0	4983.69080000000	1.39768334340	-83624.48471852001
-orient	sidtime	0	4673.71380000000	3.08138459510	251618.66692046999
-orient	sidtime	0	4138.32840000000	5.43934774160	1757.92417733000
-orient	sidtime	0	4114.82700000000	0.97343136360	-11146.28559907000
-orient	sidtime	0	3497.37870000000	0.73887625570	323421.72509830998
-orient	sidtime	0	2818.25410000000	1.33623857100	334568.01069738000
-orient	sidtime	0	2558.32340000000	3.14037501070	166573.82849543000
-orient	sidtime	0	2537.42260000000	4.29119037880	95853.55355329999
-orient	sidtime	0	2265.60960000000	1.68504052840	168669.32314357001
-orient	sidtime	0	1887.37520000000	5.57025857470	-13241.78024721000
-orient	sidtime	0	1816.57210000000	1.51174230290	85044.83842504000
-orient	sidtime	0	1402.09590000000	4.99273410410	25133.27861118000
-orient	sidtime	0	1362.06830000000	3.70947033670	5945.74918199000
-orient	sidtime	0	1345.81570000000	2.36982947630	71803.05817783999
-orient	sidtime	0	1308.84680000000	3.64799056260	-6620.89012360000
-orient	sidtime	0	1107.44410000000	1.99497976870	-72478.19911945000
-orient	sidtime	0	1020.19200000000	0.11548656780	2095.49464814000
-orient	sidtime	0	922.68640000000	2.48404819000	240472.38132141001
-orient	sidtime	0	779.04970000000	5.59991530910	-7.84495195000
-orient	sidtime	0	703.07230000000	3.09443075980	406708.63934603002
-orient	sidtime	0	675.78910000000	6.00679470100	174277.50185475001
-orient	sidtime	0	642.38020000000	6.05259017320	-65857.30899585001
-orient	sidtime	0	606.09710000000	4.83958627950	323759.29556911997
-orient	sidtime	0	584.61220000000	2.99537894890	161710.86254916000
-orient	sidtime	0	579.88670000000	4.90196440410	238714.45714407999
-orient	sidtime	0	576.00160000000	0.36392524640	179140.46780101999
-orient	sidtime	0	563.80930000000	1.58379568140	155089.97242554999
-orient	sidtime	0	516.03110000000	2.10906072550	96191.12402411000
-orient	sidtime	0	488.83780000000	5.43692539050	334905.58116818999
-orient	sidtime	0	479.80780000000	3.15587172480	-11483.85606988000
-orient	sidtime	0	420.89080000000	5.92210365350	-155765.11336717001
-orient	sidtime	0	412.67190000000	5.45481896740	-77003.59459492000
-orient	sidtime	0	380.32400000000	3.69690927330	-149144.22324357001
-orient	sidtime	0	369.63250000000	0.48609985310	77713.77144818001
-orient	sidtime	0	365.47590000000	1.20887930670	10808.71512826000
-orient	sidtime	0	354.69950000000	2.47103741190	85382.40889585001
-orient	sidtime	0	318.85230000000	5.99379743800	19187.52942919000
-orient	sidtime	0	292.86940000000	4.04065959360	251956.23739128001
-orient	sidtime	0	290.44730000000	3.87336449470	89570.23390050999
-orient	sidtime	0	265.68390000000	3.69179340690	417854.92494509002
-orient	sidtime	0	260.01650000000	4.51323974000	1420.35370652000
-orient	sidtime	0	251.55180000000	4.71307668770	233851.49119780000
-orient	sidtime	0	250.84270000000	5.32263761850	244997.77679686999
-orient	sidtime	0	238.98320000000	0.78370859050	317138.40544552001
-orient	sidtime	0	234.85740000000	1.27205990230	-5573.14279953000
-orient	sidtime	0	223.48490000000	2.07915316860	257564.41610246000
-orient	sidtime	0	215.18220000000	1.13223468610	710.17685326000
-orient	sidtime	1	474660027718929408.00000000000	0.00000000000	0.00000000000
-orient	sidtime	1	175779.87630000000	3.76126876250	-337.57047081000
-orient	sidtime	1	39643.69780000000	3.10600188250	6283.31965280000
-orient	sidtime	1	13801.45490000000	3.38603614140	18849.95895839000
-orient	sidtime	1	1973.68820000000	4.80472149130	12566.63930559000
-orient	sidtime	2	139863027.18560001254	0.00000000000	0.00000000000
-orient	sidtime	2	57463.88680000000	5.30956009070	-337.57047081000
-orient	sidtime	4	-296429.47830000002	0.00000000000	0.00000000000