static void TestFieldTransforms(EuclideanVector3 E, EuclideanVector3 B, EuclideanVector3 Ep, EuclideanVector3 Bp, EuclideanVector3 v)
{
Symbol gamma = LorentzTransform.Gamma(v);
Assert.AreEqual(Ep.ParallelComponent(v), E.ParallelComponent(v), "E Parallel component:");
Assert.AreEqual(Ep.PerpendicularComponent(v), gamma * (E + v.Cross(B)).PerpendicularComponent(v), "E Perpendicular component:");
Assert.AreEqual(Bp.ParallelComponent(v), B.ParallelComponent(v), "B Parallel component:");
Assert.AreEqual(Bp.PerpendicularComponent(v), gamma * (B - v.Cross(E)).PerpendicularComponent(v), "B Perpendicular component:");
}
public RelativisticParticle(Symbol mass, EuclideanVector3 position, Variable time)
{
this.Mass = mass;
this.Position = new LorentzVectorU(time, position);
Operator dt = new Derivative(time);
EuclideanVector3 v = dt * position;
this.Gamma = LorentzTransform.Gamma(v);
this.Velocity = this.Gamma * new LorentzVectorU(Symbol.One, v);
this.InvariantTimeDerivative = this.Gamma * dt;
}
static void TestLorentzTransform(EuclideanVector3 v)
{
LorentzVectorVariableU x0 = new LorentzVectorVariableU("t", "x", "y", "z");
LorentzVectorU x1 = x0.Transform(v);
LorentzVectorU x2 = x1.Transform(-v);
Assert.AreEqual(x0, x2);
Assert.AreEqual(LorentzMatrixUL.One, LorentzTransform.Matrix(v) * LorentzTransform.Matrix(-v));
}
public LorentzVectorOperatorU Transform(EuclideanVector3 velocity)
{
return(LorentzTransform.Matrix(velocity) * this);
}
public RelativisticParticle Transform(EuclideanVector3 velocity)
{
LorentzMatrixUL L = LorentzTransform.Matrix(velocity);
return new RelativisticParticle(this.Mass, L * this.Position, this.InvariantTimeDerivative);
}
public ElectromagneticField Transform(EuclideanVector3 velocity)
{
LorentzMatrixUL L = LorentzTransform.Matrix(velocity);
return(new ElectromagneticField(L * this.Potential, L.Invert() * this.Del));
}
public LorentzVectorL Transform(EuclideanVector3 velocity)
{
return(this * LorentzTransform.Matrix(velocity));
}
