Single-Particle Electrodynamics - Assassination Science

A.8.15
Three-velocity of a particle
The non-covariant three-velocity of a classical particle, as seen in some given
lab frame, is denoted v, and is defined as
v ≡ d t z,
(A.55)
where t is the time-coördinate in that frame.
A.8.16
MCLF of a particle
The momentarily comoving Lorentz frame, or MCLF , of a classical particle
at any given instant of time is defined to be the lab frame in which the
particle’s instantaneous three-velocity v vanishes, and its mechanical energy
is greater than zero.
The MCLF is often referred to by the alternative term instantaneous rest
frame.
Note that the MCLF is a Lorentz frame, and remains so for all time. If
the particle is being accelerated, then the MCLF at one moment will not be
the MCLF at the next instant; the latter is a new Lorentz frame.
A.8.17
CACS of a particle
The co-accelerated coördinate system of a classical particle, or CACS, is a
system of coördinates that is co-accelerated with the particle.
Unless the particle is unaccelerated for all time, the CACS does not constitute
a Lorentz frame.
A.8.18
MCLF and CACS components
Components of quantities evaluated in the MCLF (or, in general, any other
Lorentz frame) may be denoted by surrounding the dereferenced quantity by
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