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What are conditions of the equilibrium reinforce the answer with mathematical relitionship?
Wiki User
∙ 11y ago
The conditions of the equilibrium come from the conservation of Energy. Mathematically this is the the condition where the first derivative of energy is zero.
This is described for example for gravity:
Energy W = -mGM/r + cmV = -mu/r + cP = -vh/r + cP
this is the gravitational energy. Note that I have added a vector energy to Newton's potential energy, because the mass m is moving with respect to the origin. cP is the particle momentum energy.
The Equilibrium Condition is the first derivative Force, set to zero.
Force F = [d/dr, DEL][-vh/r,cP] = [vh/r2 -cDEL.P, cdP/dr - DEL vh/r + cDELxP]
At Equilibrium this expression is zero both the scalar and the vector parts.
vh/r2 - cDEL.P =0 and
cdP/dr - DEL vh/r = 0
The equilibrium conditions require v/c=1 or v=c from , vp/r = cp/r.
so v2=GM/r = c2
Wiki User
∙ 11y ago
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