FORM 4.0 (Jun 30 2012) 64-bits Run: Sat Aug 3 17:45:50 2013 * Title: SMALL CHARGED SPHERE: R(mu)*U(mu) * File: rdotu.frm * Author: David N. Williams * License: Creative Commons Attribution-Share Alike * Started: November 8, 1987 (Schoonschip) * July 7, 2012 (Form) * Revised: July 7-9,28, 2012 * * All parts of this program not in the public domain are: * * Copyright (C) 1987, 2012 David N. Williams * * This work is licensed under the Creative Commons Attribution- * Share Alike 2.5 License. To view a copy of this license, visit * http://creativecommons.org/licenses/by-sa/2.5/ or send a letter * to Creative Commons, 543 Howard Street, 5th Floor, San * Francisco, California, 94105, USA. * * Input: TAU1, TAU2, TAU3 from dtau.frm * Output: RdotU in rdotu.sav * * We need terms through eps^3 in RdotU to include the leading * nonsingular term in the Lorentz force. *** DECLARATIONS off statistics; S eps; S c,snorm; I mu,nu,l,m; V u,a,j,n; T d1y,d2y,d3y,d1u,d2u,d1a; CF R,U; Load dtau.sav; TAU1 loaded TAU2 loaded TAU3 loaded *** MODULES L dtau = TAU1*eps + TAU2*eps^2 + TAU3*eps^3; G RdotU = R(mu)*U(mu); Id 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; Id eps^4 = 0; Id 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; Id eps^4 = 0; Id u.u = c^2; Id u.a = 0; Id u.j = -a.a; Id d1u(u,l?) = 0; Id d1a(u,l?) = -d1u(a,l); Id d2u(u,l?,m?) = -d1u(nu,l)*d1u(nu,m); sum mu,nu; .sort b eps,snorm; print +s; .store dtau = + eps * ( - d1y(u,n)*c^-2 ) + eps*snorm * ( - c^-1 ) + eps^2*snorm^-1 * ( + 1/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*c^-5 - d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-3 - 1/2*d1y(u,n)*d2y(u,n,n)*c^-3 + 1/2*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-1 ) + eps^2 * ( + d1y(u,n)*d1y(a,n)*c^-4 - d1y(N1_?,n)*d1u(N1_?,n)*c^-2 - 1/2*d2y(u,n,n)*c^-2 ) + eps^2*snorm * ( + 1/2*d1y(a,n)*c^-3 ) + eps^3*snorm^-3 * ( + 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-9 - 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)* c^-7 - 1/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-7 + 1/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_? ,n)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-5 + 1/8*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*c^-5 - 1/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* c^-3 - 1/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* c^-3 - 1/4*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*c^-3 + 1/8*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)*c^-1 ) + eps^3*snorm^-2 * ( - 1/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)*c^-2 + 1/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)*c^-2 ) + eps^3*snorm^-1 * ( - 1/24*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*a.a*c^-9 - 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*c^-7 - 3/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-7 + 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*c^-5 + 1/4*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*c^-5 + 3/2*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-5 + 3/4*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-5 - 1/2*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*c^-3 - 1/2*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*c^-3 - 1/6*d1y(u,n)*d3y(u,n,n,n)*c^-3 - 1/4*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-3 - 1/2*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*c^-3 - 1/2*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-3 + 1/6*d1y(N1_?,n)*d3y(N1_?,n,n,n)*c^-1 - 1/8*d2y(u,n,n)*d2y(u,n,n)*c^-3 + 1/8*d2y(N1_?,n,n)*d2y(N1_?,n,n)*c^-1 ) + eps^3 * ( - 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*a.a*c^-8 - 1/2*d1y(u,n)*d1y(u,n)*d1y(j,n)*c^-6 - d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-6 + d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*c^-4 + 1/2*d1y(u,n)*d2y(a,n,n)*c^-4 + d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-4 + 1/2*d1y(a,n)*d2y(u,n,n)*c^-4 - 1/2*d1y(N1_?,n)*d2u(N1_?,n,n)*c^-2 - 1/2*d2y(N1_?,n,n)*d1u(N1_?,n)*c^-2 - 1/6*d3y(u,n,n,n)*c^-2 ) + eps^3*snorm * ( - 1/4*d1y(u,n)*d1y(u,n)*a.a*c^-7 - 1/2*d1y(u,n)*d1y(j,n)*c^-5 - 3/8*d1y(a,n)*d1y(a,n)*c^-5 + 1/2*d1y(N1_?,n)*d1a(N1_?,n)*c^-3 + 1/4*d2y(a,n,n)*c^-3 ) + eps^3*snorm^2 * ( - 1/6*d1y(u,n)*a.a*c^-6 - 1/6*d1y(j,n)*c^-4 ) + eps^3*snorm^3 * ( - 1/24*a.a*c^-5 ); RdotU = + eps*snorm * ( + c ) + eps^2*snorm^-1 * ( - 1/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*c^-3 + d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-1 + 1/2*d1y(u,n)*d2y(u,n,n)*c^-1 - 1/2*d1y(N1_?,n)*d2y(N1_?,n,n)*c ) + eps^2*snorm * ( + 1/2*d1y(a,n)*c^-1 ) + eps^3*snorm^-3 * ( - 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-7 + 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)* c^-5 + 1/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-5 - 1/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-3 - 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_? ,n)*c^-3 - 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-3 - 1/8*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*c^-3 + 1/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* c^-1 + 1/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* c^-1 + 1/4*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*c^-1 - 1/8*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)*c ) + eps^3*snorm^-2 * ( + 1/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n) - 1/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n) ) + eps^3*snorm^-1 * ( + 1/24*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*a.a*c^-7 + 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*c^-5 + 1/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-5 - 1/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*c^-3 - 1/4*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*c^-3 - 1/2*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-3 - 1/4*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-3 + 1/2*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*c^-1 + 1/2*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*c^-1 + 1/6*d1y(u,n)*d3y(u,n,n,n)*c^-1 - 1/4*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-1 + 1/2*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*c^-1 + 1/2*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-1 - 1/6*d1y(N1_?,n)*d3y(N1_?,n,n,n)*c + 1/8*d2y(u,n,n)*d2y(u,n,n)*c^-1 - 1/8*d2y(N1_?,n,n)*d2y(N1_?,n,n)*c ) + eps^3*snorm * ( - 1/4*d1y(u,n)*d1y(u,n)*a.a*c^-5 - 1/2*d1y(u,n)*d1y(j,n)*c^-3 - 1/8*d1y(a,n)*d1y(a,n)*c^-3 + 1/2*d1y(N1_?,n)*d1a(N1_?,n)*c^-1 + 1/4*d2y(a,n,n)*c^-1 ) + eps^3*snorm^2 * ( - 1/3*d1y(u,n)*a.a*c^-4 - 1/3*d1y(j,n)*c^-2 ) + eps^3*snorm^3 * ( - 1/8*a.a*c^-3 ); save rdotu.sav RdotU; .end 2.09 sec out of 2.09 sec