Single-Particle Electrodynamics - Assassination Science

properties of the constituent r are likewise labelled by the symbol r; or, more
frequently, by the subscript r on the quantity in question. (Note that pure
LaT E X cannot boldface an italicised subscript, and its boldfacing of roman
subscripts are of incorrect size; we therefore use the bare Roman subscript r ,
on the understanding that it is to be taken to be the three-vector r.)
Of course, the use of the rest-frame three-position r at all would be somewhat
ambiguous if the distribution of the constituents were not spherically
symmetric around the centre of energy, because an instantaneous rest frame
is only defined up to an arbitrary rotation. However, we shall only consider
spherical bodies of uniform constituent density in this thesis, and hence shall
not need to worry about such subtleties.
3.3.2 Constituent trajectories for Galilean rigidity
We now consider the problem of obtaining the trajectories of the constituents
of the rigid body. From the discussion of Section 3.2.2, we know that the
trajectory of the centre of energy of the body—in our case, the centre of the
sphere, which we shall henceforth simply refer to as “the centre”—is to be
taken as the trajectory of the body considered as a whole. The trajectories of
the other constituents must be formed in such a way so as to maintain the
spherical rest-frame three-geometry of the body.
For simplicity, we again choose our Lorentz frame according to the considerations
of Section 2.8, so that the centre of the body is instantaneously
at rest at the “zero event”. Thus, at the instant τ = 0, the four-position of
the constituent r is simply given by
t r (0) = 0,
z r (0) = r. (3.1)
Now let us first see how we would proceed if we were to assume Galilean
rigidity to hold true, rather than Einsteinian rigidity. Employing Newton’s
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