The Reference Systems and Physical Units

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| Geant 3.10  |               GEANT User's Guide              | BASE090  ##
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Author(s) : R.Brun,F.Bruyant                           Submitted: 01/10/84
Origin    : GEANT2/3                                     Revised: 10/12/92
                                  

The MAster Reference System (MARS)

The MAster Reference System (MARS) is determined by the way the user represents the kinematical quantities. If the axes are labelled (X,Y,Z), then the point P(A,B,C) is represented by

Y
 |          * P(A,B,C)
 |                     * X           A on axis X
 |                   *               B on axis Y
 |                 *                 C on axis Z
 |               *
 |             *
 |           *
 |         *
 |       *
 |     *
 |   *
 |
 -______________________________>
                               Z

The tracking is performed in the MAster Reference System. This implies that the arguments of the user magnetic field routine, space point coordinates and field components, are given in this system.

The local reference systems (MRS and DRS)

As explained in GEOM 001, the experimental setup is described by the definition of an `initial MOTHER' volume inside which `DAUGHTER' volumes are positioned. Other daughter volumes can be positioned inside these volumes which are promoted as mother volumes and so on, like Russian dolls.

This requires the definition of local reference systems, the Mother Reference Systems (MRS, Origin O ) and the Daughter Reference Systems m (DRS, Origin O ). The local reference system of the `initial mother' d

volume coincides with the MAster Reference System.

The full description of a given detector is usually given in the local reference system of the associated volume. The transformation of a point from the MRS (V ) to the DRS (V ), at any level, requires the knowledge m d of a rotation matrix R and a translation vector T defined through the relation :

    V  =[R](V  -T)
     d       m

The components of T are the projections of the vector O O onto the MRS m d axes. The rotation matrices are computed from the spherical angles of each of the axes of the daughter reference systems (I, II, III) with respect to the mother reference system (1, 2, 3). The spherical angles Theta and Phi of a direction D are defined as follows :

Theta

is the angle formed by the axis 3 and D o o (0 Phi

is the angle formed by the axis 1 and the projection of D onto the plane defined by the axes 1 and 2 o o (0

Examples are given in [GEOM200]. The various rotation matrices required for a given setup must be defined by the user during the initialisation stage. A serial number is assigned to each matrix [GEOM200]. The translation parameters and the serial number of the rotation matrix are specified by the user when the volumes are positioned inside the setup [GEOM110].

Physical units

Unless otherwise specified, the following units are used throughout the program: centimeter, second, kilogauss, GeV, GeV/c, degree.