154 lines
3.9 KiB
Mathematica
154 lines
3.9 KiB
Mathematica
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function [dLambda1,dLambda2,dz1,dz2,du1,du2,da_oa1,da_oa2] = DisturbingFunctionMultiTermVariations(n1,n2,alph,Lambda1,Lambda2,mu1,mu2,j,k,e1,e2,Pom1,Pom2,I1,I2,s1,s2,Om1,Om2,A,Ap,B,Bp,C,Cp,D,Dp,f,fE,fI,Df,DfE,DfI)
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%get the number of time stamps and number of terms, in order to replicate
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%the vectors and perform the calculation once for all terms
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% Ntime = length(Lambda1);
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% Nterm = length(k);
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%
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%
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% Lambda1 = repmat(Lambda1,1,Nterm);
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% Lambda2 = repmat(Lambda2,1,Nterm);
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% e1 = repmat(e1,1,Nterm);
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% e2 = repmat(e2,1,Nterm);
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% Pom1 = repmat(Pom1,1,Nterm);
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% Pom2 = repmat(Pom2,1,Nterm);
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% I1 = repmat(I1,1,Nterm);
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% I2 = repmat(I2,1,Nterm);
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% s1 = repmat(s1,1,Nterm);
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% s2 = repmat(s2,1,Nterm);
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% Om1 = repmat(Om1,1,Nterm);
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% Om2 = repmat(Om2,1,Nterm);
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%
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% if length(j)==length(k)
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% j = repmat(j,Ntime,1);
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% end
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% k = repmat(k,Ntime,1);
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% A = repmat(A,Ntime,1);
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% Ap = repmat(Ap,Ntime,1);
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% B = repmat(B,Ntime,1);
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% Bp = repmat(Bp,Ntime,1);
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% C = repmat(C,Ntime,1);
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% Cp = repmat(Cp,Ntime,1);
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% D = repmat(D,Ntime,1);
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% Dp = repmat(Dp,Ntime,1);
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f_inner = f+fE;
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f_outer = f+fI;
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Df_inner = Df+DfE;
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Df_outer = Df+DfI;
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% f = repmat(f,Ntime,1);
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% fE = repmat(fE,Ntime,1);
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% fI = repmat(fI,Ntime,1);
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% Df = repmat(Df,Ntime,1);
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% DfE = repmat(DfE,Ntime,1);
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% DfI = repmat(DfI,Ntime,1);
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% f_inner = repmat(f_inner,Ntime,1);
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% f_outer = repmat(f_outer,Ntime,1);
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% Df_inner = repmat(Df_inner,Ntime,1);
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% Df_outer = repmat(Df_outer,Ntime,1);
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SQ1 = sqrt(1-e1.^2);
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SQ2 = sqrt(1-e2.^2);
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%calculate the cosine argument
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Phi = j.*Lambda2+(k-j).*Lambda1-C.*Pom1-Cp.*Pom2-D.*Om1-Dp.*Om2;
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%calculate Cjk and Sjk
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PowersFactor = e1.^A.*e2.^Ap.*s1.^B.*s2.^Bp;
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Cjk = PowersFactor.*cos(Phi);
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Sjk = PowersFactor.*sin(Phi);
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%calculate the mean-motion of the longitude of conjunction
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njk = j*n2+(k-j)*n1;
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%orbital elements variations - inner planet
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da_oa1 = 2*mu2/(1+mu1)*alph*(f_inner).*(k-j)*n1./njk.*Cjk;
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dLambda1 = mu2/(1+mu1)*alph*n1./njk.*Sjk...
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.*(...
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3.*(f_inner).*(j-k)*n1./njk...
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-2*alph*(Df_inner)...
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+(f_inner).*A.*(SQ1.*(1-SQ1))./(e1.^2)...
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+(f_inner).*B/2./SQ1...
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);
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de1 = mu2/(1+mu1)*alph*(f_inner).*SQ1./e1*n1./njk.*Cjk...
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.*((j-k).*(1-SQ1)+C);
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dPom1 = mu2/(1+mu1)*alph*(f_inner)*n1./njk.*Sjk...
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.*(A.*SQ1./(e1.^2)+B/2./SQ1);
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dI1 = mu2/(1+mu1)*alph*(f_inner)./SQ1*n1./njk.*Cjk...
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.*((j-k+C).*tan(I1/2)+D./sin(I1));
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dOm1 = mu2/(1+mu1)*alph*(f_inner).*B/2.*cot(I1/2)./(SQ1.*sin(I1))*n1./njk.*Sjk;
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% dI1 = 0; dOm1 = 0;
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%orbital elements variations - outer planet
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da_oa2 = 2*mu1/(1+mu2)*(f_outer).*j*n2./njk.*Cjk;
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dLambda2 = mu1/(1+mu2)*n2./njk.*Sjk.*...
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(...
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-3*(f_outer).*j*n2./njk...
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+2*(f_outer+alph*Df_outer)...
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+(f_outer).*Ap.*SQ2.*(1-SQ2)./(e2.^2)...
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+(f_outer).*Bp/2./SQ2...
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);
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de2 = mu1/(1+mu2)*(f_outer).*SQ2./e2*n2./njk.*Cjk.*...
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(...
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-j.*(1-SQ2)+Cp...
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);
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dPom2 = mu1/(1+mu2)*(f_outer)*n2./njk.*Sjk.*...
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(...
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Ap.*SQ2./(e2.^2)+Bp/2./SQ2...
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);
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dI2 = mu1/(1+mu2)*(f_outer)./SQ2*n2./njk.*Cjk.*...
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(...
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(Cp-j).*tan(I2/2)+Dp./sin(I2)...
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);
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dOm2 = mu1/(1+mu2)*(f_outer).*Bp/2.*cot(I2/2)./(SQ2.*sin(I2))*n2./njk.*Sjk;
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% dI2 = 0; dOm2 = 0;
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NewVersion = 1;
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if ~NewVersion
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%translate to the complex form
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dz1 = (de1+1i*dPom1.*e1).*exp(1i*Pom1);
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dz2 = (de2+1i*dPom2.*e2).*exp(1i*Pom2);
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du1 = (dI1+1i*dOm1.*I1).*exp(1i*Om1);
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du2 = (dI2+1i*dOm2.*I2).*exp(1i*Om2);
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%sum the distribution of all terms to get the total effect
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dz1 = sum(dz1,2);
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dz2 = sum(dz2,2);
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du1 = sum(du1,2);
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du2 = sum(du2,2);
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da_oa1 = sum(da_oa1,2);
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da_oa2 = sum(da_oa2,2);
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dLambda1 = sum(dLambda1,2);
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dLambda2 = sum(dLambda2,2);
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else
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%translate to the complex form
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dz1 = (sum(de1,2)+1i*sum(dPom1,2).*e1).*exp(1i*Pom1);
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dz2 = (sum(de2,2)+1i*sum(dPom2,2).*e2).*exp(1i*Pom2);
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du1 = (sum(dI1,2)+1i*sum(dOm1,2).*I1).*exp(1i*Om1);
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du2 = (sum(dI2,2)+1i*sum(dOm2,2).*I2).*exp(1i*Om2);
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da_oa1 = sum(da_oa1,2);
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da_oa2 = sum(da_oa2,2);
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dLambda1 = sum(dLambda1,2);
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dLambda2 = sum(dLambda2,2);
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end
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