By Richard D. Hazeltine, Francois L. Waelbroeck
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X M .. ... ... .. . .... M g 0.. .. .. .. .. . .... ... ... . ... ... ...... .................... .......... In a constant gravitational field g 0 , the weight of a body may be viewed as concentrated at the position of the centre of mass, xM . Ö .. ... .. ... .... . ... .... . . .... ..... . . . ...... Ö Field lines follow the instantaneous field everywhere. They are very different from the orbits particles would follow through the field.
Different observers will thus agree that their respective coordinate systems are indeed Cartesian. Simple translation: A simple translation of the origin of coordinates along the x-axis by a constant Simple translation of the coordinate system by c along the x-axis. 7 Cartesian coordinate transformations We begin the analysis of coordinate transformations with the familiar elementary transformations: translation, rotation and reflection. 2), expressing the coordinates of a geometrical point in the new system as a function of the coordinates of the same point in the old.
53) In physics, the moment of inertia of an extended body and the quadrupole moment of a charge distribution are well-known tensors of second rank. Tensors of higher rank may be constructed in a similar way. A tensor of rank r has r indices and is a collection of 3r quantities that transform as the direct product of r vectors. 24). When nothing else is said, a tensor is always assumed to be of rank 2. 9 Scalar, vector and tensor fields In continuum physics the basic quantities are functions of the spatial coordinates, called fields, which may also be classified according to their behaviour under rotation.