Unfinished Conservations - Wardell Lindsay

Finishing an Unfinished Conversation

A mighty work was done by Newton
He worked without pause
Producing Three famous Laws
And little or no time for fun

Many an apple fell from the tree
Many people saw the Apple fall
But only Newton answered the call
And started the House of Gravity

Now there are seeds of madness
dark matter, dark energy
a universe of no symmetry
a place of sadness

Is conservation lost?
No! Quaternions to the rescue
Conservation of Gravity is true
Truth and beauty still the Boss.

E= -mu/r + mcV = m[-u/r,cV] Gravitational Energy
X= [d/dr, ∇] Quaternion Derivative
XE= [d/dr, ∇]m[-u/r,cV] = m[d(-u/r)/dr - c ∇.V, cdV/dr - ∇u/r + ∇xV]

The Conservation of Gravity Energy
0=XE= [d/dr, ∇]m[-u/r,cV] = m[u/r2 - c ∇.V, cdV/dr - ∇u/r ]
u/r – cv = v2 – cv =v – c=0
cdV/dr - ∇u/r = dV/dt + uR/r3 = dV/dt + w2R = 0