25Sep2015 revision 1 started (trivial changes)
	Lucas 
   Faradays_law_spherical_coordinates 

/$			∇´Ei(r´,t)      
			=		r´/r/sin(θ)	*[  ∂[∂O: sin(θ)*Ei(r´,t)•φ´] - ∂[∂P: Ei(r´,t)•O]  
				+	O/r		*[1/sin(θ)*∂[∂P: Ei(r´,t)•r´] - ∂[∂r: Ei(r´,t)•φ´]  
				+ φ´/r		*[     ∂[∂r: r*Ei(r´,t)•θ´] - ∂[∂O: Ei(r´,t)•r´]  
   
/$			 -1/c*∂[∂(t): B(r´,t)]  
			 = -v/c*r*sin(θ)*φ´*[  3*q*v/c*(r*cos(θ) - v*t)/|r - v*t|^5 
			  + 1/r/c*∂[∂(t): Ei(r - v*t,t)] ]    

/*  Looking first at (4-27)
/$			 ∇´Ei(r - v*t,t) =  -1/c*∂[∂(t): Bi(r - v*t,t)]  

/*  I will break (4-28) into parts (a)&(b), which are equal to one another.
  This section (4-28a) develops ∇´Ei(ro - vo*t,t).  
 
/$	1. ∇´Ei(r - v*t,t) term : 
/*	Generically expressing ∇´Ei(ro - vo*t,t) = ∇´Ei(r´,t) in spherical coordinates, 
   using Jackson1999 inside back cover (I removed common "r" to 
   outside of [] for e2) :

/$			∇A 
			=	 e1*/r/sin(θ)*[ ∂[∂(θ): sin(θ)*A3) -  ∂[∂(φ): A2)   ]  
			  + e2/r      *[ ∂[∂(φ): A1)/sin(θ) -  ∂[∂(r): r*A3) ]   
			  + e3/r      *[ ∂[∂(r): r*A2)    -  ∂[∂(θ): A1)   ]   
/*  Use 
/$			A1 = Ei(r´,t) in r´ direction = Ei(r´,t)•r´h   
			A2 = Ei(r´,t) in θ´ direction = Ei(r´,t)•θ´hat  
			A3 = Ei(r´,t) in φ´ direction = Ei(r´,t)•φ´hat  
/*		where the basis unit vectors are : 
/$		 	[e1,e2,e3] = [r´h,θ´hat,φ´hat]
      
/*	Notice that Lucase does NOT use "hat" notation for the angles 
	as I have used [Oh´,Ph´] - he simplifies to [Op,Pp], but to
	minimize my own confusion I retain the full notation.
	Also, Lucas retains the 1/r term within the partial derivatives for e2=Oh´,
	and I will replace r from Jackson with rs.

/$a)		∇´Ei(r - v*t,t)   
			 = + r´h/rs/sin(θ) *[ ∂[∂(θ): Ei(r´,t)•φ´hat*sin(θ)) -  ∂[∂(φ): Ei(r´,t)•θ´hat)    ]   
			 	+ θ´hat/rs      *[ ∂[∂(φ): Ei(r´,t)•r´h)/sin(θ) -  ∂(drs: Ei(r´,t)•φ´hat*rs) ]  
			   + φ´hat/rs      *[ ∂(drs: Ei(r´,t)•θ´hat*rs)   -  ∂[∂(θ): Ei(r´,t)•r´h)    ]  
			 = + r´h/rs/sin(θ) *[ ∂[∂(θ): Ei(r´,t)•φ´hat*sin(θ)) -  ∂[∂(φ): Ei(r´,t)•θ´hat)    ]  
			   + θ´hat/rs      *[ ∂[∂(φ): Ei(r´,t)•r´h)/sin(θ) -  ∂(drs: Ei(r´,t)•φ´hat*rs) ]   
			   + φ´hat/rs      *[ ∂(drs: Ei(r´,t)•θ´hat*rs)   -  ∂[∂(θ): Ei(r´,t)•r´h)    ]  


/*++++++++++++++++++++++++++++++++++++++
/*add_eqn  "Lucas_Typo_or_omission    
   04_28arev1
   Faradays_law_spherical_coordinates - full form, 1st expression  

/$			∇´Ei(r´,t)  
			= + r´h/rs/sin(θ)*[ ∂[∂(θ): Ei(r´,t)•φ´hat*sin(θ)) -  ∂[∂(φ): Ei(r´,t)•θ´hat)     ]  
			   + θ´hat/rs    *[ ∂[∂(φ): Ei(r´,t)•r´h)/sin(θ) -  ∂(drs: Ei(r´,t)•φ´hat*rs)  ]   
			   + φ´hat/rs    *[ ∂(drs: Ei(r´,t)•θ´hat*rs)   -  ∂[∂(θ): Ei(r´,t)•r´h)     ]  

/%			∇´EIodv(POIo,t)  =  -1/c*∂[∂(t): BIodv(POIp(t),t)]   
			= + Rpch(POIo(t),t) /Rocs(POIo)/sin(Aθoc(POIo))	*{ ∂[dAOoc: EIodv(POIo,t)•ROpdh*sin(Aθoc(POIo))] - ∂[dAPoc: EIodv(POIo,t)•ROpdh] }  
			   + ROpdh/Rocs(POIo)								*{ ∂[dAPch: EIodv(POIo,t)•Rpch(POIo(t),t)/sin(Aθoc(POIo))] - ∂[dRocs(POIo): EIodv(POIo,t)*Rocs(POIo)•RPods] }   
			   + Rφpdh/Rocs(POIo)								*{ ∂[dRocs(POIo): EIodv(POIo,t)•ROpdh•ROpdh] - ∂[dAOod: EIodv(POIo,t)•Rpch(POIo(t),t)] }  

/*	OK - straightforward, with a couple of concerns with Lucas's expression - reference frames & notational. 
     Note that I have taken 1/r out of the [] for Oh´ 
     plus I retain [Oh´,Ph´] within [] - Lucas simplifies to [Op,Pp]  
     But - shouldnt all angles be primed to get particle/system refFrame?  
     shouldnt there be a hat.over.last AOpdh in the second term?