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There is really only one requirement for equilibrium and it is the derivative of energy (Force) is zero, where Energy is a quaternion E=Er(eal) + Ev(ector)=Er +Ev.

0=Force=(d/dr + Del)(Er + Ev)= (dEr/dr -Del.Ev) + (dEv/dr + DelxEv + Del Er)

The two requirements then are:

dEr/dr=Del.Ev the Continuity Condition , the sum of the real forces is zero, and

0= (dEv/dr + DelxEv + Del Er) the Induction Condition or Newton's Action Reaction, the sum of the vector forces is zero.

The Continuity Condition is like the Ohms Current Node Equation and the Induction Equation is like the Ohms Voltage Loop Equation.

These two requirements involve the sum of the real forces equal zero and the sum of the vector forces equal zero for equilibrium to exist.

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