https://drive.google.com/file/d/0Bx_LsIsmyGthQzV0OFozdkt5a2c/view?usp=sharing
$ sudo apt-get install libglut3-dev
https://en.wikipedia.org/wiki/Wigner_rotation
/**
* Two general boosts Wigner https://en.wikipedia.org/wiki/Wigner_rotation
* Relativistically adds two velocities, v and u, and returns their sum, w;
* each velocity is expressed as a 3-vector in the form (x,y,z),(x,y,z);
* treats v as the velocity of a relativistic reference frame and u as the
* velocity of something within that frame
**/
static Vector3 VelocityAddition(const Vector3 &vComp,
const Vector3 &uComp,
const float &gamma_u,
const float &c)
{
float dot_VU = std::abs((uComp).Dot(vComp))/(c*c);
/**
* using the values calculated above general boosts Wigner , calculates one component at a time of
* the velocity resulting from the relativistic addition of v and u
* ------------------------------------------------------------------
* if the relativistical velocity sum is w:
* 1 gamma_u
* w = -------- * [ vComp * ( 1+dot_UV*--------- ) + uComp/gamma_u ]
* 1+dot_UV 1+gamma_u
**/
return (1.0/(1.0+dot_VU)) * (uComp * (1.f+dot_VU*(gamma_u/(1.f+gamma_u))) + (vComp/gamma_u));
}========================================================================================
/**
* class TLorentzRotation
\ingroup Physics
The TLorentzRotation class describes Lorentz transformations including
Lorentz boosts and rotations (see TRotation)
~~~
| xx xy xz xt |
| |
| yx yy yz yt |
lambda = | |
| zx zy zz zt |
| |
| tx ty tz tt |
**/
static SIMD_INLINE IMatrix4x4<T> CreateLorentzBoost( T gamma , const IVector3D<T> vel , const T &_LightSpeed = DEFAUL_LIGHT_MAX_VELOCITY_C )
{
static IMatrix4x4<T> M = IMatrix4x4<T>::IDENTITY;
const IVector3D<T> n = vel.GetUnit();
const T v = vel.Length();
//T bgamma = gamma * gamma / (1.0 + gamma);
T bgamma = (gamma - 1.0);
const T c = _LightSpeed;
M[0][0] = 1.0+((bgamma)*((n.x * n.x)));
M[1][0] = ((bgamma)*((n.y * n.x)));
M[2][0] = ((bgamma)*((n.z * n.x)));
M[3][0] = (v*n.x*gamma);
M[0][1] = ((bgamma)*((n.x * n.y)));
M[1][1] = 1.0+((bgamma)*((n.y * n.y)));
M[2][1] = ((bgamma)*((n.z * n.y)));
M[3][1] = (v*n.y*gamma);
M[0][2] = ((bgamma)*((n.x * n.z)));
M[1][2] = ((bgamma)*((n.y * n.z)));
M[2][2] = 1.0+((bgamma)*((n.z * n.z)));
M[3][2] = (v*n.z*gamma);
M[0][3] = v*n.x*gamma/(c*c);
M[1][3] = v*n.y*gamma/(c*c);
M[2][3] = v*n.z*gamma/(c*c);
M[3][3] = gamma;
}
```