/* This OLD version is WRONG! but it does reflect Lucas's recommendation 16Oct2019 This version ARBITRARILY sets ∂[∂(t): Rpcs(POIo(t),t)^(-5)*t*(cos(Aθpc(POIo(t),t)) - 1)] equal to zero, which is not actuially correct, but it does help generate the proper functional for the infinite series for E and E* THIS IS WRONG!!! - contradiction of even using sin(Aθpc(POIo(t),t))!!!! /% 1) ∂[∂(t): Rpcs(POIo(t),t)^(-5)*t*(cos(Aθpc(POIo(t),t)) - 1)] = ∂[∂(t): Rpcs(POIo(t),t)^(-5)]*t*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5)*∂[∂(t): t]*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5)*t *∂[∂(t): (cos(Aθpc(POIo(t),t)) - 1) /* for /% ∂[∂(t): Rpcs(POIo(t),t)^(-5)] /* from above somewhere : /% ∂[∂(t): Rpcs(POIo(t),t)^(-α)] = α*Vons(PART)*Rpcs(POIo(t),t)^(-α - 1)*cos(Aθpc(POIo(t),t)) /* therefore /% a) ∂[∂(t): Rpcs(POIo(t),t)^(-5)] = 5*Vons(PART)*Rpcs(POIo(t),t)^(-6)*cos(Aθpc(POIo(t),t)) b) ∂[∂(t): t] = 1 /* for ∂[∂(t): (cos(Aθpc(POIo(t),t)) - 1) /% ∂[∂(t): (cos(Aθpc(POIo(t),t)) - 1) = ∂[∂(t): (cos(Aθpc(POIo(t),t))] c) ` ∂[∂(t): (cos(Aθpc(POIo(t),t)) - 1) = (-1)*sin(Aθpc(POIo(t),t)) /* putting (a-c) into (1) /% ∂[∂(t): Rpcs(POIo(t),t)^(-5)*t*(cos(Aθpc(POIo(t),t)) - 1)] = ∂[∂(t): Rpcs(POIo(t),t)^(-5)]*t*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5)*∂[∂(t): t]*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5)*t*∂[∂(t): (cos(Aθpc(POIo(t),t)) - 1) = 5*Vons(PART)*Rpcs(POIo(t),t)^(-6)*cos(Aθpc(POIo(t),t))*t*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5) *(cos(Aθpc(POIo(t),t)) - 1) - Rpcs(POIo(t),t)^(-5)*t*sin(Aθpc(POIo(t),t)) /* HIGHLY restrictive conditions!!! - RFp = RFo, particle is at origin (both reference frames) - for a POIo along direction of flight of particle, so cos(Aθpc(POIo(t),t)) = 1 THIS IS WRONG!!! - it is contradiction of even using sin(Aθpc(POIo(t),t)) - t=0 /% ∂[∂(t): Rpcs(POIo(t),t)^(-5)*t*(cos(Aθpc(POIo(t),t)) - 1)] = 5*Vons(PART)*Rpcs(POIo(t),t)^(-6)*cos(Aθpc(POIo(t),t))*0*(cos(Aθpc(POIo(t),t)) - 1) + Rpcs(POIo(t),t)^(-5) *(1 - 1) - Rpcs(POIo(t),t)^(-5)*0*sin(Aθpc(POIo(t),t)) = 0 /* the second derivative in 4-33 work file Equation (4) is ARBITRARILY set = 0 therefore K1 = 0