C SMALL CHARGED SPHERE: Lorentz Force F(mu,nu)*U(nu), leading non-singular order, near field only File: lnear Input: tau1.o, tau2.o, tau3.o from dtau.z RdotA from RdotA.z denom2, denom3 from denoms.z Output: Starting date: November 8, 1987 Last revision: November 18, 1987 Enter dtau.z ! Load tau1.o, tau2.o, tau3.o Enter denoms.z Enter RdotA.z Names tau1.o,tau2.o,tau3.o,RdotA,denom2,denom3 A dtau=4,eps=4 A c I mu,nu V u,a,j,n F D1y,D2y,D3y,D1u,D2u,D1a A norm Common tau1.o,tau2.o,tau3.o Common RdotA,denom2,denom3 X R(mu) = - D1y(mu,n)*eps - D2y(mu,n,n)*eps^2/2 - D3y(mu,n,n,n)*eps^3/6 - u(mu)*dtau - D1u(mu,n)*eps*dtau - D2u(mu,n,n)*eps^2*dtau/2 - a(mu)*dtau^2/2 - D1a(mu,n)*eps*dtau^2/2 - j(mu)*dtau^3/6 X U(mu) = u(mu) + D1u(mu,n)*eps + D2u(mu,n,n)*eps^2/2 + a(mu)*dtau + D1a(mu,n)*eps*dtau + j(mu)*dtau^2/2 X A(mu) = a(mu) + D1a(mu,n)*eps + j(mu)*dtau *fix A eps=4 ! eps^3 is leading nonsingular order in this section B eps X F(mu,nu) = [ R(mu)*U(nu) - R(nu)*U(mu) ] * d3 * c^2 Z f = F(mu,u) ! Lorentz force density Id, uDu = c^2 Id, uDa = 0 Id, uDj = -aDa Id, D1u(u,l~) = 0 Id, D1a(u,l~) = -D1u(a,l) C Id, D2u(u,l~,m~) = -D1u(nu,l)*D1u(nu,m) Id, dtau = tau1.o*eps + tau2.o*eps^2 + tau3.o*eps^3 C Vicious Id,! C Id, D1y(mu~,n~)*D1y(mu~,n~) = - norm*norm + D1y(u,n)*D1y(u,n)/c^2 *yep Id, Commu, D1y,D2y,D3y,D1u,D2u,D1a *yep Id, d2 = denom2 *yep Id, Commu, D1y,D2y,D3y,D1u,D2u,D1a *yep Id, d3 = denom3 *yep Id, Commu, D1y,D2y,D3y,D1u,D2u,D1a Id, eps = 0 ! superfluous order from RdotA Id, eps^-1 = 0 ! kill singular orders Id, eps^-2 = 0 *yep Id, D1y(mu,n) = eta(mu,n) + D1y(u,n)*u(mu)*c^-2 *yep Id, norm^-7 = 0 ! kill odd powers of n Id, norm^-5 = 0 Id, norm^-3 = 0 Id, norm^-1 = 0 Id, uDu = c^2 *yep Id,Commu, D1y *yep Id,Commu, D1y *end