Single-Particle Electrodynamics - Assassination Science

6.5.7 Computer algebra
All of the quantities listed to this point were originally calculated by hand, by
the author, to the full order of ε indicated. It should be apparent, upon reflection
of the lengthy nature of the explicit expressions listed in Appendix G,
why it was not feasible to continue to compute such expressions by hand.
Thus, the author decided to investigate methods of calculating and verifying
the algebra by computational means. A description of this investigation
is given in Section G.2 of Appendix G.
From this point, the expressions listed in Section G.6 were calculated to
one lower order by hand; the computer algebra programs verified these lowerorder
results, as well as providing the next order of terms. Only one error
was found in the manually-computed expressions, that had not yet been used
for any consequential computations. Once the error in the manual expression
had been located and corrected, the computer algebra program was used to
verify the electric charge field results through to completion (which had also
been completed, manually), and to compute, for the first time, the dipole
field and radiation reaction results.
6.5.8 Gamma factor
Returning, now, to the algebraic derivation, we note that two terms in the
retarded field expressions of Chapter 5 involve the Lorentz gamma factor γ ret ;
however, it will be noted that, in both cases, it appears in the form
γ −2
ret ≡ 1 − v 2 ret.
To compute γ −2
ret , we use (6.56); the result (to the lower order of ε actually
required for this particular quantity) is
γ −2
ret = 1 − r 2 d ˙v2 + r 3 d ( ˙v·¨v) + r 2 d r s ˙v 2 (n s· ˙v) + · · · + O(ε 6 ). (6.62)
259