/run/media/bill/PROJECTS/Lucas - Universal Force/individual formulae developments/z_Archive/04_34 dimensions.txt
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29Aug2019 Dimensional check : THIS IS VERY OLD :
Dimensional consistency check :
Force (F) units - ??? see "Howell - Variables, notations, styles for Bill Lucas, Universal Force.odt"
/$ 15/2*β^3*q*rs^4/|r - v*t|^7*sin(θ)^2*cos(θ)
/* charge
OOPS! I cant get F units to balance yet in any case (see "Howell - Variables, notations, styles for Bill Lucas, Universal Force.odt")
Simpler approach - just look at terms in Lucas's equation :
/$a) Eis(r - v*t,t) APPLY |t=0 TO EACH TERM
= charge/length^2
β) =+ 3/2*β^2*q *rs^3 /|r - v*t|^5*sin(θ)^2 - λ(v)*q *rs /|r - v*t|^3
charge*length^3/ length^5 - charge*length/ length^3
= charge/length^2 - charge/length^2
= charge/length^2
/* OK - same as (a) E
/$c) + β *rs^2*∫[∂(θ),0 to Of: sin(θ)*
length^2*
(+ 15/2*β^3*q*rs^4 /|r - v*t|^7*sin(θ)^2*cos(θ)
charge*length^4/length^7 = charge/length^3
- 3 *β *q*rs^2/|r - v*t|^5*λ(v) *cos(θ)
charge*length^2/length^5 = charge/length^3
/* overall for (c) = charge/length
WRONG - missing /length
However, my results WILL WORK here! (one less power of length)
/$∂) + β^2 *rs^4*∫[∂(θ),0 to Of: 1/rs/c*sin(θ)*∂[∂(t):
length^4 /length /time
∫[∂(θ),0 to Of: 1/rs/c*sin(θ)*∂[∂(t): Eis(r - v*t,t)])])
/length /time*(charge/length^2)
/* overall for (d) = charge/time^2
WRONG - this part is way off! (????)
my dimensional analysis here is wrong and incomplete....