Detailed Description

Trk::RungeKuttaUtils is set algorithms for track parameters transformation from local to global and global to local system coordinate and step estimation to surface.

AtaPlane AtaStraightLine AtaDisc AtaCylinder Perigee | | | | | | | | | |

V V V V V

| Local->Global transformation V Global position (Runge Kutta presentation) |

V Global->Local transformation

| | | | | | | | | | V V V V V PlaneSurface StraightLineSurface DiscSurface CylinderSurface PerigeeSurface

For using Runge Kutta method we use global coordinate, direction, inverse momentum and Jacobian of transformation. All this parameters we save in array P[42]. /dL0 /dL1 /dPhi /dThe /dCM X ->P[0] dX / P[ 7] P[14] P[21] P[28] P[35] Y ->P[1] dY / P[ 8] P[15] P[22] P[29] P[36] Z ->P[2] dZ / P[ 9] P[16] P[23] P[30] P[37] Ax ->P[3] dAx/ P[10] P[17] P[24] P[31] P[38] Ay ->P[4] dAy/ P[11] P[18] P[25] P[32] P[39] Az ->P[5] dAz/ P[12] P[19] P[26] P[33] P[40] CM ->P[6] dCM/ P[13] P[20] P[27] P[34] P[41]

where in case local presentation

L0 - first local coordinate (surface dependent) L1 - second local coordinate (surface dependent) Phi - Azimuthal angle The - Polar angle CM - charge/momentum

in case global presentation

X - global x-coordinate = surface dependent Y - global y-coordinate = surface dependent Z - global z-coordinate = sutface dependent Ax - direction cosine to x-axis = Sin(The)*Cos(Phi) Ay - direction cosine to y-axis = Sin(The)*Sin(Phi) Az - direction cosine to z-axis = Cos(The) CM - charge/momentum = local CM

Author: Igor..nosp@m.Gavr.nosp@m.ilenk.nosp@m.o@ce.nosp@m.rn.ch