/*+-----+
From Lucas's book : 10Jan2017 corrections
p68h0.0 Equation (4-16), with my more up-to-date symbols, and removing redundant "c"'s (and using BT = B0 + BI, but B0 = 0) : 
/%(4-16) 	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)/c*Rpcs(POIo(t),t)*sin(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)*Vons(PART)/Rpcs(POIo(t),t)^5*[Rpcs(POIo(t),t)*cos(Aθpc(POIo(t),t)) - Vons(PART)*t]
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Rpcs(POIo(t),t)
	  }   
	=   Vons(PART)/c*Rpcs(POIo(t),t)*sin(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)*Vons(PART)/Rpcs(POIo(t),t)^5*Rpcs(POIo(t),t)*cos(Aθpc(POIo(t),t)) 
	   -  3*Q(PART)*Vons(PART)/Rpcs(POIo(t),t)^5*Vons(PART)*t
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Rpcs(POIo(t),t)
	  }   
	=   Vons(PART)/c*sin(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)*Vons(PART)  *cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t)^3  
	    - 3*Q(PART)*Vons(PART)^2*t                /Rpcs(POIo(t),t)^4
	    - ∂[∂(t): EIpds(POIo(t),t)]
	  }   
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)*cos(Aθpc(POIo(t),t)) /Rpcs(POIo(t),t)^3  
	    - 3*Q(PART)*Vons(PART)  *t/Rpcs(POIo(t),t)^4
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)
	  }   
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  
	    - 3*Q(PART) /Rpcs(POIo(t),t)^3
	       *Vons(PART)  *t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t)
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   
	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  
	     *[1 -  Vons(PART)*t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) ]
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   

Summarizing : 
(1) 	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)/Rpcs(POIo(t),t)^3  *[1 -  Vons(PART)*t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) ]
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   

/*+--+
15&16May2016 But looking at : 
/%	Vons(PART) *t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t)

From "Rθ0pcs(POIo(t),t)", RFo basis :
	(1)*	Rθ0pcs(POIo(t),t) = Rocs(POIo)*cos(Aθoc(POIo)) - Vons(PART)*t
From "Rθ0pcs(POIo(t),t)", RFp basis
	(1)**	Rθ0pcs(POIo(t),t) = Rpcs(POIo(t),t)*cos(Aθpc(POIo(t),t))
combining (1)* & (1)** : 
	   Rocs(POIo)*cos(Aθoc(POIo)) - Vons(PART)*t
	=  Rpcs(POIo(t),t)*cos(Aθpc(POIo(t),t))
So : 
	Vons(PART)*t
	=  Rocs(POIo)*cos(Aθoc(POIo)) - Rpcs(POIo(t),t)*cos(Aθpc(POIo(t),t))
or : 
	Vons(PART)*t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t)
	=  Rocs(POIo)*cos(Aθoc(POIo))/Rpcs(POIo(t),t)/cos(Aθpc(POIo(t),t)) - 1 
(2)	=  Rθ0ocs(POIo)/Rθ0pcs(POIo(t),t) - 1 

Subbing (2) into (1) : 
	(1) 	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  *[1 -  Vons(PART)*t/cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) ]
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  *[ 1 -  Rθ0ocs(POIo)/Rθ0pcs(POIo(t),t) - 1 ]
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   

Summarizing :  
(3) 	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  *Rθ0ocs(POIo)/Rθ0pcs(POIo(t),t)
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   


/*********************
Compare this to :  

/*********************
>>>>>>>>> ∂[∂(t): BTodv(POIo,t)]  = ∂[∂(t): BTpdv(POIo(t),t)] without use of Lenz's Induction Law (need to RE-CHECK!!!)


/*Howell's expression Section "∂[∂(t): BTodv(POIo,t)]  = ∂[∂(t): BTpdv(POIo(t),t)] without use of Lenz's Induction Law (need to RE-CHECK!!!)"
/%(6)*	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)  /Rpcs(POIo(t),t)^3  11Jan2017 WRONG UNITS!!!
	   -    EIpds(POIo(t),t)/Rpcs(POIo(t),t)  
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t)) 
	  }   

/*While the factor of 3 IS EXPLAINED, this is NOT the same as (3) in the sub-sub-section immediately above, as I have in (6)* an extra term for ∂[∂(t): E0] at right angles to Rodh(Vonv_X_Rpcv(POIo)), due to angular changes.  However, it's hard to tell given the term EIpds(POIo(t),t)/Rpcs(POIo(t),t).

By applying Lenz's Law : 

From "Lenz's Induction Law and it's context" based on Lucas p70h0.85 Equation (4-31) :  
/%(4-31)	EIpds(POIo(t),t)*Rpch(POIo(t),t)
	= -λ(Vons(PART))*E0ods(POIo)*Rpch(POIo(t),t) 
and therefore : 
	EIpds(POIo(t),t)  = -λ(Vons(PART))*E0ods(POIo) 

From "E0odv(POIp(t),t) = E0pdv(POIp)"  :  
	(1)*	E0pdv(POIp) =  E0odv(POIp(t),t)
	= Q(PART)/Rpcs(POIp)^2*Rpch(POIp) 
Subbing (1)* into (4-31)* : 
	(4-31)	EIpds(POIo(t),t)*Rpch(POIo(t),t)
	= -λ(Vons(PART))*E0ods(POIo)*Rpch(POIo(t),t) 
(1)	= -λ(Vons(PART))*Q(PART)/Rpcs(POIp)^2*Rpch(POIo(t),t) 

Subbing (1) into (6)* : 
	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)  /Rpcs(POIo(t),t)^3
	   -    EIpds(POIo(t),t)/Rpcs(POIo(t),t)  
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t)) 
	  }   
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)  /Rpcs(POIo(t),t)^3
	   -   (-λ(Vons(PART))*Q(PART)/Rpcs(POIp)^2)/Rpcs(POIo(t),t)  
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t)) 
	  }   
/*Do I have a mistake with the sign here?

/*Summarizing to yield Howell's expression Section "∂[∂(t): BTodv(POIo,t)]  = ∂[∂(t): BTpdv(POIo(t),t)] subbing for Lenz's Law : 
/%(2)	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)  /Rpcs(POIo(t),t)^3  *[1 + λ(Vons(PART))/3]  
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t)) 
	  }   

/*Substituting for lambda from Lucas p73h0.7 in the text : 
/%	lambda = β^2  =  (Vons(PART)/c)^2






/*+-----+
REPEATING results for ease of comparison : 

From Lucas (4-16), sub-sub-section above : 
/%(3) 	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART) /Rpcs(POIo(t),t)^3  *Rθ0ocs(POIo)/Rθ0pcs(POIo(t),t)
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))
	  }   


/*Howell's expression Section "∂[∂(t): BTodv(POIo,t)]  = ∂[∂(t): BTpdv(POIo(t),t)] subbing for Lenz's Law : 
/%(2)	∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)] 
	=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo(t),t))
	 *{   3*Q(PART)  /Rpcs(POIo(t),t)^3  *[1 + λ(Vons(PART))/3]  
	   -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t)) 
	  }   


/*These are "somewhat similar", and the factor of 3 is explained.  However, there are very important differences, as highlighted above.

As for the cause of the discrepancy, that is not fully clear : 
As per above "...   While the factor of 3 IS EXPLAINED, this is NOT the same as (3) in the sub-sub-section immediately above, as I have in (6)* an extra term for ∂[∂(t): E0] at right angles to Rodh(Vonv_X_Rpcv(POIo)), due to angular changes.   ..." 
perhaps there is also a difference between point-particle and finite-sized derivations, as I have not yet done the latter?  But this is not obvious from Lucas' book.