/run/media/bill/PROJECTS/Lucas - Universal Force/individual formulae developments/z_Archive/04_34 dimensions.txt


/*-----+
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....