Lucas's derivation :  

/$		∂[∂t: Bi(r - v*t,t))  
		= ∂[∂(t): Bi(r - v*t,t)] + (v•∇´)*Bi(r - v*t,t)  
		= ∂[∂(t): Bi(r - v*t,t)] + ∇´   [Bi(r - v*t,t)v] + v* [∇´•Bi(r - v*t,t)]  
		= ∂[∂(t): Bi(r - v*t,t)] + ∇´   [Bi(r - v*t,t)v]   

/*  since ∇´•Bi = 0  

  Irrelevant : 
  04_19 Point charge with symmetry @ v_const, add Faradays law (Ampere!)  
/$			∮[•d(l´),.over.L: (Ei´(r´,t´) - v/cBi(r´,t´))) = -1/c*     ∫[dAreap,.over.Ap: (∂[∂(t): Bi(r - v*t,t)]•n)
/*  04_20 Convective_derivative  
/$			∂/∂(t) = ∂[∂t:  + v•∇´
/*  Apply Lucas's (4-20) to Lucas's (4-19) 
/$			(∂[∂t:  + v•∇´))


/* First try - Howells derivation
  Apply Lucas's (4-20) convDeriv to Bi(ro - vo*t,t) B total, observer frame)
/$			∂/∂(t)[Bi(r - v*t,t)] = (∂[∂t:  + v•∇´)[Bi(r - v*t,t)]  
/$			∂/∂(t)[Bi(r - v*t,t)] =  ∂[∂(t): Bi(r - v*t,t)] + (v•∇´)[Bi(r - v*t,t)]  

/*	Vector operations from Jackson1999 inside front cover 
/$			∇(a•β) = (a•∇)*β + (β•∇)*a + a(∇β) + β(∇a)
/*  therefore 
/$			(a•∇)β = ∇(a•β) - [+ (β•∇)*a + a(∇β) + β(∇a) ] 
/*  HOWEVER - I dont fully comprehend the form (a•∇´)b, presumably eg 
/$			(a•∇) = (a1*n1 + a2*n2 + a3*n3) • (∂/∂x1*n1 + ∂/∂x2*n2 + ∂/∂x3*n3)
			(a•∇) = (a1*∂/∂x1 + a2*∂/∂x2 + a3*∂/∂x3) 
/* therefore 
/$			(a•∇)β = (a1*∂/∂x1     + a2*∂/∂x2     + a3*∂/∂x3) * β 
/* but what does that "*b" mean? - assume "kind of" a dot product ???
/$			(a•∇)β =  a1*∂/∂x1(b1) + a2*∂/∂x2(b2) + a3*∂/∂x3(b3)
/*   take 
/$			a = v, β 
			=					 Bi(r - v*t,t), ∇ = ∇´
					(v•∇´)*	[Bi(r - v*t,t)] 
			= + 		∇(v•	 Bi(r - v*t,t)) 
			  - [	+			(Bi(r - v*t,t)•∇)*v 
					+ v(∇	 Bi(r - v*t,t)) 
					+			 Bi(r - v*t,t)(∇v) 
				 ]  
/*	Oops, wrong one
/$			∇(aβ) = a*(∇•β) - β*(∇•a) + (β•∇)*a - (a•∇)*β
/* therefore 
/$			(a•∇)β	= a*(∇•β) - β*(∇•a) + (β•∇)*a - ∇(aβ)
/* again, take a = v, b =  Bi(ro - vo*t,t), ∇ = ∇´
/$			(v•∇´)			 Bi(r - v*t,t) 
			= + v(∇´•Bi(r - v*t,t)) 
			  -			 Bi(r - v*t,t)(∇´•v) 
			  +			(Bi(r - v*t,t)•∇´)v 
			  - ∇´(v	 Bi(r - v*t,t))
/*	Using ∇´•B = 0, ∇´v = 0 for constant relative v
/$			(v•∇´)*	 Bi(r - v*t,t) 
			= -       Bi(r - v*t,t)(∇´•v) 
			  - ∇´(vBi(r - v*t,t))

/*	Summarizing Howells development :  
/$			∂/∂(t)[Bi(r - v*t,t)] =  ∂[∂(t): Bi(r - v*t,t)] + (v•∇´)[Bi(r - v*t,t)]  
			∂/∂(t)[Bi(r - v*t,t)] 
			=   ∂[∂(t): Bi(r - v*t,t)] 
			  - Bi(r - v*t,t)(∇´•v) 
/*	rearrange 
/$			∂/∂(t)[Bi(r - v*t,t)] =  ∂[∂(t): Bi(r - v*t,t)] - ∇´(vBi(r - v*t,t)) - Bi(r - v*t,t)(∇´•v)  

  Can I combine? : - ∇´(vBi(r - v*t,t)) - Bi(r - v*t,t)(∇´•v) 
  From Kreyszig 
/$			aβ = - βa
/* Try 
/$			β(c∂) = (β∂)c - (βc)∂ on 
			∇´(vBi(r - v*t,t)) = (∇´.Bi(r - v*t,t))*v - (∇´.v)*Bi(r - v*t,t) 
/* but 
/$			∇´.Bi(r - v*t,t) = 0 
/*	so 
/$			∇´(vBi(r - v*t,t)) = 0 - (∇´.v)*Bi(r - v*t,t)
/*  putting this in 
/$			  - ∇´(v		Bi(r - v*t,t)) - Bi(r - v*t,t)*(∇´•v)
			= - [- (∇´.v)*	Bi(r - v*t,t)] - Bi(r - v*t,t)*(∇´•v)
			= 0 
/*	OOPS - that wiped me out!  -should check why some day, wheres my mistake?
  
 2nd try - Howells derivation
   Apply Lucas's (4-20) convDeriv to Bi(ro - vo*t,t) B total, observer frame)

/$			∂/∂(t)[Bi(r - v*t,t)] = (∂[∂t:  + v•∇´)[Bi(r - v*t,t)]  
			∂/∂(t)[Bi(r - v*t,t)] =  ∂[∂(t): Bi(r - v*t,t)] + (v•∇´)[Bi(r - v*t,t)]  

/*	scalar triple products   Kreyszig Section 5.9 p213-216
/$			β(c∂) = (β∂)*c - (βc)*∂  
			(β∂))*c = β(c∂) + (βc)*∂  
/* again, take b = ∇´, c = Bi(ro - vo*t,t), d = v
			(∇´v)Bi(ro - vo*t,t) = ∇´(Bi(ro - vo*t,t)v) + (∇´Bi(ro - vo*t,t))*v so 
/*	OK - this looks closer?  
/$	Given ∇´Bi(r - v*t,t) = 0 then 
			(∇´v)Bi(r - v*t,t) = ∇´(Bi(r - v*t,t)v) + 0 
/*	such that 
/$			∂/∂(t)[Bi(r - v*t,t)] =  ∂[∂(t): Bi(r - v*t,t)] + ∇´[Bi(r - v*t,t)v]  


/*++++++++++++++++++++++++++++++++++++++
/*add_eqn  "no_issue       
   04_21 
   convective derivative of Total magnetic flux density Bi  

/$		∂/∂(t)[Bi(r - v*t,t)] = ∂[∂(t): Bi(r - v*t,t)] + ∇´[Bi(r - v*t,t)v]   
		∂/∂(t)[Bi(r - v*t,t)] = ∂[∂(t): Bi(r - v*t,t)] + ∇´[Bi(r - v*t,t)v] 

/%^%		d/∂(t)[BIodv(ro - vo*t,t)] = ∂[∂(t): BIodv(ro - vo*t,t)] + ∇´[BIodv(ro - vo*t,t)Vonv(PART)]   
		dT[∂(t): BIodv(POIo,t)] = ∂[∂(t): BIodv(POIo,t)] + ∇´[BIodv(POIo,t)Vons(PART)]  

/*  OK - 2nd try gets same as Lucas 
   HOWEVER -  I should have been using convective derivatives elsewhere!! - eg as I did with dp[dt : E] 
   (eg file "Howell - Background math for Lucas Universal Force, Chapter 4.odt")