Reference frame beam coordinate system

Fig. 1.9. Reference frames (a) global coordinate system and (b) beam coordinate system...

In a crossed-beam experiment the angular and velocity distributions are measured in the laboratory coordinate system, while scattering events are most conveniently described in a reference frame moving with the velocity of the centre-of-mass of the system. It is thus necessary to transfonn the measured velocity flux contour maps into the center-of-mass coordmate (CM) system [13]. Figure B2.3.2 illustrates the reagent and product velocities in the laboratory and CM coordinate systems. The CM coordinate system is travelling at the velocity c of the centre of mass... 

Eq. 4.1 can be obtained from several mechanics textbooks (e.g., [20, 21]) and is shown here in 3-dimensional vector notation under consideration of relative motion. J is the matrix of the probe mass s moment of inertia 0,2 and eo0,2 are the angular acceleration and velocity of the probe mass s coordinate system (index 2) with respect to the inertial frame (index 0) 0,i and (001 are the angular acceleration and velocity of the reference system (index 1) with respect to the inertial frame. The reference system is attached to the sensing element s substrate and therefore also to the vehicle whose motion is to be measured. 2 and oi12 belong to the probe mass with respect to the reference system. M is the torque applied to the probe mass and is composed of the driving stimulus as well as the stiffness of the suspension beams and the damping of the mechanical resonator. 

Molecular beam experiments are performed in a laboratory frame of reference but the chemically interesting events take place with respect to the center of mass of the colliding species. In order to interpret the data, differential cross sections measured in the laboratory (LAB) coordinate system must be transformed to reflect events which took place in the center-of-mass (CM) coordinate system. To effect this transformation the invariant motion of the center of mass must be subtracted from the scattering data obtained in the LAB system. A simple example which illustrates the difference between LAB and CM kinematics is shown, for an elastic collision, in Fig. 8.6. In CM the particles always move directly toward one another before interaction and directly apart afterwards. This condition is a consequence of momentum conservation in a system with a stationary center of mass. The interaction causes each particle to be deflected through... 

Thus, the considered moving reference frame agrees with the coordinate system introduced to describe the beam. Therein the position of an arbitrary... 

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