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EqSPZonal.m
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EqSPZonal.m
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%% EqSPZonal
% Desc: Computes 2nd order Short-period effects for Jn (n >= 3) for Equinoctial elements.
% Equinoctial elements: [a l+g+h tan(i/2)*cos(h) tan(i/2)*sin(h) e*cos(g+h) e*sin(g+h)];
% Reference:
% B. Mahajan, S. R. Vadali and K. T. Alfriend, �Analytic Solution For Satellite
% Relative Motion: The Complete Zonal Gravitational Problem,� 26th AAS/AIAA
% Space Flight Mechanics Meeting, Napa, CA, February 2016.
% Author: Bharat Mahajan (https://github.com/princemahajan)
function [EqSP, Dsp] = EqSPZonal(Xm,degree,mu,Re,Jcoeff,InverseOn, JacobianOn, tol)
% The following value will be returned by beta, betaSP functions in case
% the divide by 0 singularity occurs in these functions.
ERR_VAL = -999999999;
O2Msign = 1;
if InverseOn == true
O2Msign = -1;
end
% for each zonal
narr = 3:1:degree;
J2 = Jcoeff(2);
a = Xm(1); Lambda = Xm(2); p1 = Xm(3); p2 = Xm(4); q1 = Xm(5); q2 = Xm(6);
DelXm = Del2Eqn(Xm,mu,true);
l = DelXm(1); g = DelXm(2); h = DelXm(3);L = DelXm(4);G =DelXm(5); H= DelXm(6);
e = sqrt(q1^2 + q2^2);
eta = sqrt(1 - e^2);
i = 2*atan(sqrt(p1^2 + p2^2));
si = sin(i);
ci = cos(i);
ch = cos(h);
sh = sin(h);
si2 = sin(i/2);
ci2 = cos(i/2);
% intermediate quantities
psi = Mean2TrueLong(Lambda, q1, q2, tol);
lop = mod(atan2(q2,q1),2*pi);
f = psi - lop;
Psi = psi;
Delta = atan((tan(Psi)-tan(Lambda))/(1+tan(Psi)*tan(Lambda)));
dfdl = (1 + e*cos(f))^2/eta^3;
dfde = (2+e*cos(f))*sin(f)/eta^2;
d2fdfdlbye = -2*(1+e*cos(f))*sin(f)/eta*3;
d2fdfdl = e*d2fdfdlbye;
d2fdfdldfdlbye = 1/2/eta^6*((3*eta^2-7)*sin(f) + e*(eta^2-7)*sin(2*f) + (3*eta^2-3)*sin(3*f) ...
+ e/2*(eta^2-1)*sin(4*f));
d2fdl2bye = d2fdfdldfdlbye;
d2fdl2 = e*d2fdl2bye;
dfdlm1bye = 2*cos(f)/eta^3 + 1/2*e*cos(2*f)/eta^3 + 1/2*e*(2*eta^2 + 3*eta + 3)/(1+eta)/eta^3;
d2fdlde = 1/2/eta^5*((9-5*eta^2)*cos(f) - e*(eta^2-7)*cos(2*f) + (3-3*eta^2)*cos(3*f) ...
- e/2*(eta^2-1)*cos(4*f) - e/2*(eta^2 - 9));
fLG = -sqrt((1-eta)/(1+eta))*sin(f)*(2+e*cos(f))/G;
fLGdfbye = (-2*cos(f)-e*cos(2*f))/L/eta/(1+eta);
fLGdf = fLGdfbye*e;
dfLGde = 1/2/sqrt(mu*a)/eta^3*((3*eta^2-4*eta-3)*sin(f)/(1+eta) - e*(eta+5)*sin(2*f)/(1+eta) ...
+ 3*(eta-1)*sin(3*f) + 1/2*(eta-1)*e*sin(4*f));
fLGbye = 1/L/(1+eta)/eta*(-2*sin(f) - 1/2*e*sin(2*f));
dfdlfLGbye = dfdl*fLGbye;
d2fdfde = -e * sin(f) ^ 2 / eta ^ 2 + (0.2e1 + e * cos(f)) * cos(f) / eta ^ 2;
dfdee = 1/eta^4*(4*e*sin(f) + 1/2*(-eta^2 + 2)*sin(2*f));
d2fde2 = d2fdfde*dfde + dfdee;
% J2 Equinoctial First Order Short-Period Effects (Using Maple)
% J2 Equinoctial Second Order Short-Period Effects (Using Maple)
% Second order Short-Period effects due to higher degree zonals
EqSP = zeros(6,1);
Dsp = zeros(6);
for ctr = 1:length(narr)
n = narr(ctr);
Jn = Jcoeff(n);
% Short-period Effects on Equinoctial elements
% intermediate terms
[K2n,K2nk1bye,K2nk2bye] = getK2nF(@dummy, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[K2nLGH,K2nLGHk1bye] = getK2nF(@KLGHfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[K2nn2j,~,~] = getK2nF(@n2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2nn2jbysi = getK2nF(@n2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[K2ngbysi,K2ngk1byebysi,~] = getK2ngF(@dummy,n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2ng = K2ngbysi*si;
K2ngk1bye = K2ngk1byebysi*si;
K2neGH1 = getK2nF(@KeGHfunc1, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[~,K2neGH2,~] = getK2nF(@KeGHfunc2, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2neGH = K2neGH1 + K2neGH2;
W1 = sqrt(a^3/mu)*Delta*K2n;
[W2W3f, W2W3fk1bye, W2W3fk2bye] = getW2W3f(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
W2n2jW3bysi = getW2W3F(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2n2jW3 = W2n2jW3bysi*si;
W2W3gbysi = getW2W3g(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2W3g = W2W3gbysi*si;
W2eW3 = getW2eW3F(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
W2iW3 = getW2iW3(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
[W1lge, W1lgel] = getW1lge(n,Jn,J2,a,e,eta,i,f,l,g,G,Delta,mu,Re,K2n, K2ngk1bye);
W23lge = getW23lge(@dummy,n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re,false);
% SMA
ansp2 = -2*sqrt(a/mu)*(sqrt(a^3/mu)*(dfdl-1)*K2n + W2W3f*dfdl);
% MAOL
[W2Lt3W3,~,~] = getW2W3F(@Lt3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
Lambdasp2 = 3/L*W1 + sqrt(a^3/mu)*(Delta*K2nLGH + K2n*fLG) - W2Lt3W3 + W2W3f*fLG;
% Inclination terms p1 p2
if ci == 0
p1sp2 = 0;
p2sp2 = 0;
else
t1p12 = ci/G/(1+ci);
t2p12o = sqrt(a^3/mu)*Delta*(-K2nn2jbysi) - W2n2jW3bysi;
t3p12o = sqrt(a^3/mu)*Delta*K2ngbysi + W2W3gbysi;
p1sp2 = t1p12*(-sh*t2p12o - ch*t3p12o);
p2sp2 = t1p12*(ch*t2p12o - sh*t3p12o);
end
% Eccentricity terms q1 q2
t1q12o = sqrt(a^3/mu)*(Delta*K2neGH - dfde*eta/L*K2n);
t2q12o = -eta/L*W2eW3 - e/G/(1+ci)*W2iW3 - eta/L*dfde*W2W3f;
t3q12o = W1lge + W23lge;
q1sp2 = -sin(g+h)*(t1q12o + t2q12o) - cos(g+h)*t3q12o;
q2sp2 = cos(g+h)*(t1q12o + t2q12o) - sin(g+h)*t3q12o;
JnSP = [ansp2, Lambdasp2, p1sp2,p2sp2,q1sp2,q2sp2]';
EqSP = EqSP + JnSP;
if JacobianOn ~= true
continue;
end
% Generate D matrix
% intermediate terms
[K2ngbysi,K2ngk1byebysi,~] = getK2ngF(@dummy,n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2ngbye = K2ngk1byebysi*si;
[~,K2nk1byek,~] = getK2nF(@kfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2ne = (2*n-1)*e/eta^2*K2n + K2nk1byek;
[~,K2nk1byekn2j,~] = getK2nF(@kn2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2nen2j = (2*n-1)*e/eta^2*K2nn2j + K2nk1byekn2j;
[~,K2ngk1byek,~] = getK2ngF(@kfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2nge = (2*n-1)*e/eta^2*K2ng + K2ngk1byek;
dK2ndi = ci*K2nn2jbysi;
K2nLGHn2jbysi = getK2nF(@KLGHn2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2nLGHdi2 = getK2nF(@KLGHdi2func, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
dK2nLGHdi = ci*K2nLGHn2jbysi + K2nLGHdi2;
K2nn2jbysi = getK2nF(@n2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[K2nLGHgbysi,K2nLGHgk1bysibye,~] = getK2ngF(@KLGHfunc,n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[~,K2nLGHk1byek] = getK2nF(@KLGHkfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2nLGHe = (2*n-1)*e/eta^2*K2nLGH + e/eta^2*K2nLGH + K2nLGHk1byek;
K2nn2jn2jbysi = getK2nF(@n2jn2jfunc, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[K2ngn2jbysi,K2ngn2jk1byebysi,~] = getK2ngF(@n2j1func,n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[K2ng2bysi,K2ng2k1byebysi,~] = getK2ng2F(@dummy, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2ngn2jbye = K2ngn2jk1byebysi*si;
K2neGH1ibysi = getK2nF(@KeGHfunc1i, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[~,K2neGH2ibysi,~] = getK2nF(@KeGHfunc2i, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2neGH3i = getK2nF(@KeGHfunc3i, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2neGHi = (K2neGH1ibysi + K2neGH2ibysi)*si + K2neGH3i;
K2neGHg1bysi = getK2ngF(@KeGHfunc1, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
[~,K2neGHg2k1byebysi] = getK2ngF(@KeGHgfunc2, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,true);
K2neGHgbysi = K2neGHg1bysi + K2neGHg2k1byebysi;
K2nSPeGHe1 = getK2nF(@KeGHefunc1, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[~,K2neGHek1bye,~] = getK2nF(@KeGHefunc2, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[~,~,K2neGHek2bye] = getK2nF(@KeGHefunc3, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
K2neGHe = (2*n*e/eta^2)*K2neGH + K2nSPeGHe1 + K2neGHek1bye + K2neGHek2bye;
W1lbye = sqrt(a^3/mu)*K2n*dfdlm1bye;
W1l = W1lbye*e;
W1n2jbysi = sqrt(a^3/mu)*Delta*K2nn2jbysi;
W1gbysi = sqrt(a^3/mu)*Delta*K2ngbysi;
W1e = sqrt(a^3/mu)*(dfde*K2n + Delta*K2ne);
W1gbye = sqrt(a^3/mu)*(f-l)*K2ngk1bye;
W1lgei = getW1lgei(n,Jn,J2,a,e,eta,i,f,l,Delta, g,G,mu,Re,dK2ndi);
[W1lgegbysi] = getW1lgeg(n,Jn,J2,a,e,eta,i,f,l,Delta,g,G,mu,Re,K2ngbysi);
[W1lgee] = getdW1lgede(n,Jn,J2,a,e,eta,i,f,l,Delta,g,G,mu,Re,K2n,K2ne,dfde);
W2iW3fbysi = getW2iW3f(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2iW3f = W2iW3fbysi*si;
[W2W3fgbysi,W2W3fgk1byebysi,W2W3fgk2byebysi] = getW2W3fg(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2W3fg = W2W3fgbysi*si;
W2W3fgk1bye = W2W3fgk1byebysi*si;
W2W3fgk2bye = W2W3fgk2byebysi*si;
W2eW3f = getW2eW3fF(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
[W2W3f2,W2W3f2k1bye,W2W3f2k2bye] = getW2W3f2(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
[W2W3fn2jbysi,W2W3fn2jk1byebysi,~] = getW2W3f(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
W2W3fn2j = W2W3fn2jbysi*si;
W2W3fn2jk1bye = W2W3fn2jk1byebysi*si;
W2n2jn2jW3bysi = getW2W3F(@n2jn2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
[W2n2jW3gbysi,W2n2jW3gk1byebysi,~] = getW2W3g(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
[W2W3g2bysi,W2W3g2k1byebysi,W2W3g2k2byebysi] = getW2W3g2(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2W3g2k2bye = W2W3g2k2byebysi*si;
W2en2jW3 = getW2eW3F(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
W23lgel = getW23lgel(n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re,dfdl,d2fdfdl,false);
W2eiW3 = ci*getW2eW3F(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2i2W3 = W2n2jn2jW3bysi*ci^2;
W23lgei = ci*getW23lge(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re,true);
W2iW3gbysi = getW2iW3g(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2iW3g = W2iW3gbysi*si;
W2eW3gbysi = getW2eW3gF(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2eW3g = W2eW3gbysi*si;
W23lgegbysi = getW23lgeg(@dummy,n,Jn,J2,a,e,eta,i,f,l,g,L,G,dfdl,mu,Re);
W2e2W3 = getW2e2W3F(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
[W2W3,~,~] = getW2W3F(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
[~,~,W2W3k2byek] = getW2W3F(@kterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
W23lgee = getdW23lgede(n,Jn,J2,a,e,eta,i,f,l,g,L,G,W23lge,mu,Re,dfdl,dfde,d2fdlde);
% K2nSPgbye = getK2nSPgbyeF(@dummy,n,Jn,J2,a,e,eta,i,g,mu,Re);
% K2nSPge = (2*n-1)*e/eta^2*K2nSPg + getK2nSPgF(@kfunc,n,Jn,J2,a,e,eta,i,g,mu,Re);
% [K2nSPg2,K2nSPg2bye] = getK2nSPg2F(@dummy,n,Jn,J2,a,e,eta,i,g,mu,Re);
% W2eW3g = getW2eW3g(n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% [W2n2jW3g,W2n2jW3gk1bye] = getW2W3g(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2W3g2m1 = getW2W3g2m1F(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2iW3gSI = getW2iW3gSI(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% SMA Row
% da
daspda = -(n-1)/a*ansp2;
% dL
daspdL = -2*sqrt(a/mu)*(sqrt(a^3/mu)*K2n*d2fdl2 + W2W3f*d2fdl2 + W2W3f2*(dfdl)^2);
% dp1 dp2
dW2diW3f = W2iW3fbysi;
daspdi = -2*sqrt(a/mu)*(sqrt(a^3/mu)*(dfdl-1)*dK2ndi + dW2diW3f*dfdl);
daspdgbysi = -2*sqrt(a/mu)*(sqrt(a^3/mu)*(dfdl-1)*K2ngbysi + W2W3fgbysi*dfdl);
daspdp1 = daspdi*(1+ci)*ch + daspdgbysi*(1+ci)*sh;
daspdp2 = daspdi*(1+ci)*sh - daspdgbysi*(1+ci)*ch;
% dq1 dq2
daspde = -2*sqrt(a/mu)*(sqrt(a^3/mu)*(dfdl-1)*K2ne + sqrt(a^3/mu)*K2n*d2fdlde ...
+ W2eW3f*dfdl + W2W3f2*dfde*dfdl + W2W3f*d2fdlde);
daspdlq12 = -2*sqrt(a/mu)*(sqrt(a^3/mu)*d2fdl2bye*K2n + W2W3f*d2fdl2bye + W2W3f2k1bye*dfdl^2);
daspdgq12 = -2*sqrt(a/mu)*(sqrt(a^3/mu)*dfdlm1bye*K2ng + W2W3fgk1bye*dfdl);
W2k0W3f2fg = -2*sqrt(a/mu)*dfdl*dfdlm1bye*getW2k0F(@k0dadldadgterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
daspdq1 = daspde*cos(g+h) + daspdlq12*sin(g+h) - daspdgq12*sin(g+h) + W2k0W3f2fg*sin(g+h);
daspdq2 = daspde*sin(g+h) - daspdlq12*cos(g+h) + daspdgq12*cos(g+h) - W2k0W3f2fg*cos(g+h);
% Mean Longitude Row
[W2Lt3W3f,W2Lt3W3fk1bye] = getW2W3f(@Lt3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
W2Lt3W3n2jbysi = getW2W3F(@Lt3n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2Lt3W3i2 = getW2W3F(@Lt3i2func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
[W2Lt3W3gbysi,W2Lt3W3gk1byebysi] = getW2W3g(@Lt3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,true);
W2eLt3W3 = getW2eW3F(@Lt3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
W2Lt3W3e2 = getW2W3F(@Lt3e2func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
% da
dLspda = 3/L/2/a*W1*(-2*n) + Delta*K2nLGH/2*sqrt(a/mu)*(-2*n) + K2n*fLG*sqrt(a/mu)*(-n) ...
+ 2*n/2/a*W2Lt3W3 - (2*n-1)/2/a*W2W3f*fLG - 1/2/a*W2W3f*fLG;
% dLambda
dLspdL = 3/L*W1l + sqrt(a^3/mu)*(dfdlm1bye*e*K2nLGH + K2n*fLGdf*dfdl) - W2Lt3W3f*dfdl ...
+ W2W3f2*dfdl*fLG + W2W3f*dfdl*fLGdf;
% dp1 dp2
dLspdi = 3/L*W1n2jbysi*ci + sqrt(a^3/mu)*(Delta*dK2nLGHdi + K2nn2jbysi*ci*fLG) ...
- W2Lt3W3n2jbysi*ci - W2Lt3W3i2 + W2W3fn2jbysi*ci*fLG;
dLspdgbysi = 3/L*W1gbysi + sqrt(a^3/mu)*(Delta*K2nLGHgbysi + K2ngbysi*fLG) ...
- W2Lt3W3gbysi + W2W3fgbysi*fLG;
dLspdp1 = dLspdi*ch*(1+ci) + dLspdgbysi*sh*(1+ci);
dLspdp2 = dLspdi*sh*(1+ci) - dLspdgbysi*ch*(1+ci);
% dq1 dq2
dLspde = 3/L*W1e + sqrt(a^3/mu)*(Delta*K2nLGHe + dfde*K2nLGHe + K2ne*fLG + K2n*dfLGde) ...
- W2eLt3W3 - W2Lt3W3*e/eta^2 - W2Lt3W3e2 + W2eW3f*fLG + W2W3f2*dfde*fLG + W2W3f*dfLGde;
dLspdl = 3/L*W1lbye + sqrt(a^3/mu)*(dfdlm1bye*K2nLGH + K2n*fLGdfbye*dfdl) - W2Lt3W3fk1bye*dfdl ...
+ W2W3f2*dfdlfLGbye + W2W3f*dfdl*fLGdfbye;
dLspdg = 3/L*W1gbye + sqrt(a^3/mu)*(Delta*K2nLGHgk1bysibye*si + K2ngbye*fLG)...
- W2Lt3W3gk1byebysi*si + W2W3fg*fLGbye;
W2Lt3W3fgk0 = -getW2k0F(@k0W2Lt3W3fgterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re)*dfdlm1bye;
dLspdq1 = dLspde*cos(g+h) + dLspdl*sin(g+h) - dLspdg*sin(g+h) + W2Lt3W3fgk0*sin(g+h);
dLspdq2 = dLspde*sin(g+h) - dLspdl*cos(g+h) + dLspdg*cos(g+h) - W2Lt3W3fgk0*cos(g+h);
% Incination row p1,p2
% da
dp1spda = -n/a*(p1sp2);
dp2spda = -n/a*(p2sp2);
% dL
t1 = ci/G/(1+ci);
t2 = sqrt(a^3/mu)*dfdlm1bye*e*(-K2nn2j) - W2W3fn2jbysi*si*dfdl;
t3 = sqrt(a^3/mu)*dfdlm1bye*e*K2ng + W2W3fg*dfdl;
dp1spdL = t1*(-sh*t2 - ch*t3);
dp2spdL = t1*(ch*t2 - sh*t3);
% dp1 dp2
dp1spdi = -si/G/(1+ci)^2*(-sh*t2p12o - ch*t3p12o) ...
+ t1p12*(-sh*(sqrt(a^3/mu)*Delta*(-K2nn2jn2jbysi*ci) - W2n2jn2jW3bysi*ci) ...
-ch*(sqrt(a^3/mu)*Delta*K2ngn2jbysi*ci + W2n2jW3gbysi*ci) );
dp1spdg = t1p12*(-sh*(sqrt(a^3/mu)*Delta*(-K2ngn2jbysi) - W2n2jW3gbysi) ...
-ch*(sqrt(a^3/mu)*Delta*K2ng2bysi + W2W3g2bysi));
dp1spdh = t1p12*(-ch*(sqrt(a^3/mu)*Delta*(-K2nn2jbysi) - W2n2jW3bysi) ...
+ sh*(sqrt(a^3/mu)*Delta*K2ngbysi) + W2W3gbysi);
dp1spdp1 = dp1spdi*ch*(1+ci) + dp1spdg*sh*(1+ci) - dp1spdh*sh*(1+ci);
dp1spdp2 = dp1spdi*sh*(1+ci) - dp1spdg*ch*(1+ci) + dp1spdh*ch*(1+ci);
dp2spdi = -si/G/(1+ci)^2*(ch*t2p12o - sh*t3p12o) ...
+ t1p12*(ch*(sqrt(a^3/mu)*Delta*(-K2nn2jn2jbysi*ci) - W2n2jn2jW3bysi*ci) ...
-sh*(sqrt(a^3/mu)*Delta*K2ngn2jbysi*ci + W2n2jW3gbysi*ci) );
dp2spdg = t1p12*(ch*(sqrt(a^3/mu)*Delta*(-K2ngn2jbysi) - W2n2jW3gbysi) ...
-sh*(sqrt(a^3/mu)*Delta*K2ng2bysi + W2W3g2bysi));
dp2spdh = t1p12*(-sh*(sqrt(a^3/mu)*Delta*(-K2nn2jbysi) - W2n2jW3bysi) ...
- ch*(sqrt(a^3/mu)*Delta*K2ngbysi) + W2W3gbysi);
dp2spdp1 = dp2spdi*ch*(1+ci) + dp2spdg*sh*(1+ci) - dp2spdh*sh*(1+ci);
dp2spdp2 = dp2spdi*sh*(1+ci) - dp2spdg*ch*(1+ci) + dp2spdh*ch*(1+ci);
% dq1 dq2
dp1spde = t1p12*e/eta^2*(-sh*t2p12o - ch*t3p12o) ...
+ t1p12*(-sh*(sqrt(a^3/mu)*dfde*(-K2nn2j) + sqrt(a^3/mu)*Delta*(-K2nen2j) ...
- W2en2jW3 - W2W3fn2j*dfde) -ch*(sqrt(a^3/mu)*dfde*K2ng ...
+ sqrt(a^3/mu)*Delta*K2nge + W2eW3g + W2W3fg*dfde));
dp1spdg = t1p12*(-sh*(sqrt(a^3/mu)*Delta*(-K2ngn2jbye) - W2n2jW3gk1byebysi*si) ...
-ch*(sqrt(a^3/mu)*Delta*K2ng2k1byebysi*si + W2W3g2k1byebysi*si));
dp1spdl = t1p12*(-sh*(sqrt(a^3/mu)*(dfdlm1bye)*(-K2nn2j) - W2W3fn2jk1bye*dfdl) ...
-ch*(sqrt(a^3/mu)*(dfdlm1bye)*K2ng + W2W3fgk1byebysi*si*dfdl));
dp1spdlgk0term = t1p12*getW2k0F(@dp1spdlgk0func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dp1spdlg2k0term = t1p12*getW2k0F(@dp1spdlg2k0func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dp1spdq1 = dp1spde*cos(g+h) - dp1spdg*sin(g+h) + dp1spdl*sin(g+h) ...
+ dp1spdlgk0term*sh*dfdlm1bye*sin(g+h) + dp1spdlg2k0term*ch*dfdlm1bye*sin(g+h);
dp1spdq2 = dp1spde*sin(g+h) + dp1spdg*cos(g+h) - dp1spdl*cos(g+h) ...
- dp1spdlgk0term*sh*dfdlm1bye*cos(g+h) - dp1spdlg2k0term*ch*dfdlm1bye*cos(g+h);
dp2spde = t1p12*e/eta^2*(ch*t2p12o - sh*t3p12o) ...
+ t1p12*(ch*(sqrt(a^3/mu)*dfde*(-K2nn2j) + sqrt(a^3/mu)*Delta*(-K2nen2j) ...
- W2en2jW3 - W2W3fn2j*dfde) -sh*(sqrt(a^3/mu)*dfde*K2ng ...
+ sqrt(a^3/mu)*Delta*K2nge + W2eW3g + W2W3fg*dfde));
dp2spdg = t1p12*(ch*(sqrt(a^3/mu)*Delta*(-K2ngn2jbye) - W2n2jW3gk1byebysi*si) ...
-sh*(sqrt(a^3/mu)*Delta*K2ng2k1byebysi*si + W2W3g2k1byebysi*si));
dp2spdl = t1p12*(ch*(sqrt(a^3/mu)*(dfdlm1bye)*(-K2nn2j) - W2W3fn2jk1bye*dfdl) ...
- sh*(sqrt(a^3/mu)*(dfdlm1bye)*K2ng + W2W3fgk1byebysi*si*dfdl));
dp2spdlgk0term = t1*getW2k0F(@dp1spdlgk0func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dp2spdlg2k0term = t1*getW2k0F(@dp1spdlg2k0func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dp2spdq1 = dp2spde*cos(g+h) - dp2spdg*sin(g+h) + dp2spdl*sin(g+h) ...
- dp2spdlgk0term*ch*dfdlm1bye*sin(g+h) + dp2spdlg2k0term*sh*dfdlm1bye*sin(g+h);
dp2spdq2 = dp2spde*sin(g+h) + dp2spdg*cos(g+h) - dp2spdl*cos(g+h) ...
+ dp2spdlgk0term*sh*dfdlm1bye*cos(g+h) - dp2spdlg2k0term*ch*dfdlm1bye*cos(g+h);
% Eccentricity terms row q1,q2
% da
dq1spda = -n/a*q1sp2;
dq2spda = -n/a*q2sp2;
% dL
t1dl = sqrt(a^3/mu)*(dfdlm1bye*e*(K2neGH) - d2fdlde*eta/L*K2n);
t2dl = -eta/L*W2eW3f*dfdl - e/G/(1+ci)*W2iW3fbysi*si*dfdl - eta/L*d2fdlde*W2W3f - eta/L*dfde*W2W3f2*dfdl;
t3dl = W1lgel + W23lgel;
dq1spdL = -sin(g+h)*(t1dl + t2dl) - cos(g+h)*t3dl;
dq2spdL = cos(g+h)*(t1dl + t2dl) - sin(g+h)*t3dl;
% dp1 dp2
t1isi = sqrt(a^3/mu)*(Delta*(K2neGHi) - dfde*eta/L*K2nn2jbysi*ci);
t2isi = -eta/L*W2eiW3 - e/G/(1+ci)*W2i2W3 + e/G*W2iW3*si/(1+ci)^2 - eta/L*dfde*W2iW3fbysi;
t3isi = W1lgei + W23lgei;
dq1spdi = - sin(g+h)*(t1isi + t2isi) - cos(g+h)*t3isi;
t1g = sqrt(a^3/mu)*(Delta*(K2neGHgbysi) - dfde*eta/L*K2ngbysi);
t2g = -eta/L*W2eW3gbysi - e/G/(1+ci)*W2iW3gbysi - eta/L*dfde*W2W3fgbysi;
t3g = W1lgegbysi + W23lgegbysi;
dq1spdgbysi = (-cos(g+h)*(t1q12o + t2q12o) + sin(g+h)*t3q12o)*0 + (-sin(g+h)*(t1g + t2g) - cos(g+h)*t3g);
dq1spdhbysi = (-cos(g+h)*(t1q12o + t2q12o) + sin(g+h)*t3q12o)*0;
dq1spdp1 = dq1spdi*ch*(1+ci) + dq1spdgbysi*(1+ci)*sh - dq1spdhbysi*(1+ci)*sh;
dq1spdp2 = dq1spdi*sh*(1+ci) - dq1spdgbysi*(1+ci)*ch + dq1spdhbysi*(1+ci)*ch;
dq2spdi = cos(g+h)*(t1isi + t2isi) - sin(g+h)*t3isi;
dq2spdgbysi = (-sin(g+h)*(t1q12o + t2q12o) - cos(g+h)*t3q12o)*0 + (cos(g+h)*(t1g + t2g) - sin(g+h)*t3g);
dq2spdhbysi = (-sin(g+h)*(t1q12o + t2q12o) - cos(g+h)*t3q12o)*0;
dq2spdp1 = dq2spdi*ch*(1+ci) + dq2spdgbysi*(1+ci)*sh - dq2spdhbysi*(1+ci)*sh;
dq2spdp2 = dq2spdi*sh*(1+ci) - dq2spdgbysi*(1+ci)*ch + dq2spdhbysi*(1+ci)*ch;
% dq1 dq2
dqdqss1 = a/mu*((e/2*(4*eta^2+9*eta+9)/(1+eta)/eta^4)*cos(f) + 1/2*((7-eta^3-eta^2)/eta^4*cos(2*f)) ...
+ 3/2*e*cos(3*f)/eta^4 + 1/4*(1-eta^4)/eta^4*cos(4*f) ...
+ (9 + 9*eta-eta^2-7*eta^3-6*eta^4-4*eta^5)/4/eta^4/(1+eta))*K2n;
dbgterm = getW2k0F(@dqdqss1t2,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dbgt2 = 1/(2*eta^4*L)*(e*(4*eta^2+9*eta+9)*cos(f)/(1+eta) - (eta^3+eta^2-7)*cos(2*f) ...
+ 3*e*cos(3*f) - 1/2*(eta^2 - 1)*cos(4*f) - (6*eta^3+eta^2-9)/2);
[~,~,W2W3fk2bye2q1q1sst2] = getW2W3f(@q1q1sst2nkterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
q1q1sst2w2k = getW2kF(@q1q1sst2w2kterm,n,1,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqss2 = (2*n-1)/eta^2*W2W3f*dfdl*eta/sqrt(mu*a) + eta/sqrt(mu*a)*d2fdfde*W2W3fk1bye*dfdl ...
+ dbgterm*dbgt2 + W2W3fk2bye2q1q1sst2*eta/L*dfdl ...
+ q1q1sst2w2k*1/2*eta/sqrt(mu*a)*dfdl*(n-1)*sqrt((1-eta)/(1+eta));
[~,~,W2W3gk2bye2q1q1sst3] = getW2W3g(@q1q1sst3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,false);
dqdqss3 = -(2*n-1)/G*W2W3g - eta/L*W2W3gk2bye2q1q1sst3;
q1q1sst4 = getW2k0F(@q1q1sst4term,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqss4 = eta/L*dfde*(W2W3f2k1bye*dfdl - W2W3fgk1bye) + eta/L*dfde*dfdlm1bye*q1q1sst4;
[~,q1q1sst5k1bye,~] = getK2ngF(@q1q1sst5term1, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
[~,~,q1q1sst5k2bye] = getK2ngF(@q1q1sst5term2, n,Jn,J2,a,e,eta,i,g,G,f,mu,Re,false);
dqdqss5 = Delta*a/mu*(q1q1sst5k1bye + q1q1sst5k2bye);
dqdqssrest = -sqrt(a^3/mu)*dfdlm1bye*K2neGH + 1/eta^2/(1+ci)*(W2iW3f*dfdl - W2iW3g)*eta/L ...
- eta/L*sqrt(a^3/mu)*dfde*K2ngbye;
dqdqss = dqdqss1 + dqdqss2 + dqdqss3 + dqdqss4 + dqdqss5 + dqdqssrest;
dqdqcs12t1 = getW2k0F(@q1q1cs12t1,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs12t2 = getW2k0F(@q1q1cs12t1,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs12t3 = getdqdqcst123(@dummy, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
dqdqcs1 = (f-l)*a/(mu*eta)*(dqdqcs12t1 + (n-1)/2*dqdqcs12t2 + dqdqcs12t3);
dqdqcs2 = a/2/mu/eta^4*(e/(1+eta)*(4*eta^2+7*eta+7)*sin(f) - (eta^3+eta^2-7)*sin(2*f) ...
+ 3*e*sin(3*f) + 0.5*e^2*sin(4*f))*K2n ...
+ K2ngbye*a/(2*mu*eta)*(4*cos(f)+e*cos(2*f) + e*(2*eta^2+3*eta+3)/(1+eta)) ...
- a*eta/mu*dfdlm1bye*K2ngk1bye;
dqdqscK3 = -sqrt(a^3/mu)*(f-l)*K2neGHe + sqrt(a^3/mu)*(-dfde*K2neGH - e/G*dfde*K2n + eta/L*d2fde2*K2n ...
+ dfde*eta/L*K2ne);
dqdqsc4 = -e/G*W2eW3 - e^2/eta^3/L/(1+ci)*W2iW3 -e/G*dfde*W2W3f ...
+ eta/L*(W2e2W3 + 1/eta^2/(1+ci)*W2iW3 + e/eta^2/(1+ci)*W2eiW3 + 2*e^2/eta^4*W2iW3) ...
+ eta/L*(W2eW3f + e/eta^2/(1+ci)*W2iW3f)*dfde ...
+ eta/L*(d2fde2*W2W3f + dfde*W2eW3f + dfde*W2W3f2*dfde);
dqdqcs4 = -eta/L/eta^2/(1+ci)*W2iW3;
dfdl2etam1 = 1/eta^5*(e*(eta^4+eta^3+eta^2+eta+1)/(1+eta) + 4*cos(f) + 6*e*(cos(f))^2 ...
+ 4*e^2*(cos(f))^3 + e^3*(cos(f))^4);
dqdqcs5sf = 2/L*dfdl2etam1*eta*sin(f)*getW2k0F(@q1q1sc5sfterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs5s1pc = 1/L*getW2k0F(@q1q1sc5s1pcterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs5s1mc = 1/L*getW2k0F(@q1q1sc5s1mcterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
cs5cfgterm = 1/2/eta^4*(e/(1+eta)*(4*eta^2 + 7*eta +7)*sin(f) + (7-eta^2-eta^3)*sin(2*f) ...
+ 3*e*sin(3*f) + e^2*sin(4*f)/2);
dqdqcs5cfg = 1/L*cs5cfgterm*getW2k0F(@q1q1sc5cfgterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs5cfg2 = -dfdlm1bye/2/eta/L*(4*cos(f)+e*cos(2*f)+3*e)...
*getW2k0F(@q1q1sc5cfg2term,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs5w3fg = W2W3fgk2bye*eta^2/L*dfdl*(1 + 1/eta);
dqdqcs5w3g2 = W2W3g2k2bye*eta^2/L*(-1/eta);
dqdqcs5w3f2 = W2W3f2k2bye*eta^2/L*(-dfdl^2);
dqdqcs5w3f = -W2W3fk2bye*eta^2/L*d2fdl2;
dqdqcs5cf = -eta^2/L*(n-1)/2*2*cos(f)*d2fdfdldfdlbye*getW2k0F(@q1q1sc5cfterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs51pc1mc = -eta^2/L*(n-1)/2*getW2k0F(@q1q1sc51pc1mcterm,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
dqdqcs5 = -eta/L*(2*n-1)/eta^2*W2W3 + W2W3k2byek + dqdqcs5sf + dqdqcs5s1pc + dqdqcs5s1mc ...
+ (-eta/L)*(dfde*W2W3fk1bye) + dqdqcs5cfg + dqdqcs5cfg2 + dqdqcs5w3fg + dqdqcs5w3g2 + dqdqcs5w3f2 ...
+ dqdqcs5w3f + dqdqcs5cf + dqdqcs51pc1mc;
dqdqcs = dqdqcs1 + dqdqcs2 + dqdqcs4 + dqdqcs5;
dqdqsc = dqdqscK3 + dqdqsc4;
dqdqcc = -W1lgee - W23lgee;
dq1spdq1 = sin(g+h)*sin(g+h)*dqdqss + sin(g+h)*cos(g+h)*dqdqsc ...
+ cos(g+h)*sin(g+h)*dqdqcs + cos(g+h)*cos(g+h)*dqdqcc;
dq1spdq2 = -sin(g+h)*cos(g+h)*dqdqss + sin(g+h)*sin(g+h)*dqdqsc ...
- cos(g+h)*cos(g+h)*dqdqcs + si*cos(g+h)*sin(g+h)*dqdqcc;
dq2spdq1 = -cos(g+h)*sin(g+h)*dqdqss - cos(g+h)*cos(g+h)*dqdqsc ...
+ sin(g+h)*sin(g+h)*dqdqcs + sin(g+h)*cos(g+h)*dqdqcc;
dq2spdq2 = cos(g+h)*cos(g+h)*dqdqss - cos(g+h)*sin(g+h)*dqdqsc ...
- sin(g+h)*cos(g+h)*dqdqcs + sin(g+h)*sin(g+h)*dqdqcc;
% D matrix
Dspn = [daspda, daspdL, daspdp1, daspdp2, daspdq1, daspdq2;
dLspda, dLspdL, dLspdp1, dLspdp2, dLspdq1, dLspdq2;
dp1spda, dp1spdL, dp1spdp1, dp1spdp2, dp1spdq1, dp1spdq2;
dp2spda, dp2spdL, dp2spdp1, dp2spdp2, dp2spdq1, dp2spdq2;
dq1spda, dq1spdL, dq1spdp1, dq1spdp2, dq1spdq1, dq1spdq2;
dq2spda, dq2spdL, dq2spdp1, dq2spdp2, dq2spdq1, dq2spdq2];
Dsp = Dsp + Dspn;
end
% % Total First Order SP contributions
% EqSPX1 = J2_SPX1;
%
% % Total Second Order SP contributions
% EqSPX2 = J2_SPX2 + J2^2/2*Jn_SPX2;
%
% EqSPX = EqSPX1 + EqSPX2;
EqSP = O2Msign*J2^2/2*EqSP;
Dsp = O2Msign*J2^2/2*Dsp;
end
% function ansp2 = getanSP2(n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re)
%
% ansp2 = 0;
% if sin(i) == 0
% return;
% end
%
% dfdl = (1 + e*cos(f))^2/eta^3;
% K2nSP = getK2nSPF(@dummy, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% W2W3f = getW2W3f(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
%
% ansp2 = -2*sqrt(a/mu)*sin(i)*(sqrt(a^3/mu)*(dfdl-1)*K2nSP + W2W3f*dfdl);
%
% end
%
% function Lambdasp2 = getLambdaSP2(n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re)
%
% Lambdasp2 = 0;
% if sin(i) == 0
% return;
% end
%
% fLG = -sqrt((1-eta)/(1+eta))*sin(f)*(2+e*cos(f))/G;
% K2nSP = getK2nSPF(@dummy, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% K2nSPLGH = getK2nSPF(@KLGHfunc, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% W2W3f = getW2W3f(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2Lt3W3 = getW2W3F(@Lt3func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W1 = sqrt(a^3/mu)*(f-l)*K2nSP;
%
% Lambdasp2 = sin(i)*(3/L*W1 + sqrt(a^3/mu)*((f-l)*K2nSPLGH + K2nSP*fLG) - W2Lt3W3 + W2W3f*fLG);
%
% end
%
function Lt3 = Lt3func(n,j,k,a,e,eta,i,ci,G,f,g)
Lt3 = 1/G*((2*n-1) + (n-2*j)*ci/(1+ci) + k*eta^2/(1+eta));
end
function Lt3 = Lt3n2jfunc(n,j,k,a,e,eta,i,ci,G,f,g)
Lt3 = Lt3func(n,j,k,a,e,eta,i,G,ci)*(n-2*j);
end
function Lt3 = Lt3i2func(n,j,k,a,e,eta,i,ci,G,f,g)
Lt3 = 1/G*(-sin(i)/(1+ci)^2);
end
function Lt3 = Lt3e2func(n,j,k,a,e,eta,i,ci,G,f,g)
Lt3 = 1/G*(-e*(eta+2)*k/(1+eta^2));
end
%
% function [p1sp2,p2sp2] = getp1p2SP2(n,Jn,J2,a,e,eta,i,f,l,g,h,L,G,mu,Re)
%
% p1sp2 = 0; p2sp2 = 0;
% if cos(i) == 0
% return;
% end
%
% % K2nSP = getK2nSPF(@dummy, n,Jn,J2,a,eta,i,g,mu,Re);
% K2nSPn2j = getK2nSPF(@n2jfunc, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% W2n2jW3 = getW2W3F(@n2jfunc,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2W3g = getW2W3g(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% K2nSPg = getK2nSPg(n,Jn,J2,a,e,eta,i,g,mu,Re);
%
% t1 = cos(i)/2/G/((cos(i/2))^2);
% t2 = sqrt(a^3/mu)*(f-l)*(-K2nSPn2j) - W2n2jW3;
% t3 = sqrt(a^3/mu)*(f-l)*K2nSPg + W2W3g;
%
% p1sp2 = t1*(-sin(h)*t2 - cos(h)*t3);
% p2sp2 = t1*(cos(h)*t2 - sin(h)*t3);
%
% end
%
% function [q1sp2,q2sp2] = getq1q2SP2(n,Jn,J2,a,e,eta,i,f,l,g,h,L,G,mu,Re)
%
% q1sp2 = 0; q2sp2 = 0;
% if sin(i) == 0
% return;
% end
%
% dfde = (2+e*cos(f))*sin(f)/eta^2;
% K2nSP = getK2nSPF(@dummy, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% K2nSPeGH1 = getK2nSPF(@KeGHfunc1, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% K2nSPeGH2 = getK2nSPFk1(@KeGHfunc2, n,Jn,J2,a,e,eta,i,g,G,mu,Re);
% K2nSPeGH = K2nSPeGH1 + K2nSPeGH2;
% W2eW3 = getW2eW3(n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2iW3SI = getW2iW3SI(n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W2W3f = getW2W3f(@dummy,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re);
% W1lge = getW1lge(n,Jn,J2,a,e,eta,i,f,l,g,G,mu,Re);
% W23lge = getW23lge(n,Jn,J2,a,e,eta,i,f,l,g,L,G,mu,Re);
%
% t1 = sqrt(a^3/mu)*((f-l)*(K2nSPeGH) - dfde*eta/L*K2nSP);
% t2 = -eta/L*W2eW3 - e/2/G/((cos(i/2))^2)*W2iW3SI - eta/L*dfde*W2W3f;
% t3 = W1lge + W23lge;
%
% q1sp2 = sin(i)*(-sin(g+h)*(t1 + t2) - cos(g+h)*t3);
% q2sp2 = sin(i)*(cos(g+h)*(t1 + t2) - sin(g+h)*t3);
%
% end
function n2j = n2jfunc(n,j,k,a,e,eta,i,ci,G,f,g)
n2j = n-2*j;
end
function k1 = kfunc(n,j,k,a,e,eta,i,ci,G,f,g)
k1 = k;
end
function k1 = kn2jfunc(n,j,k,a,e,eta,i,ci,G,f,g)
k1 = k*(n-2*j);
end
function n2j1 = n2j1func(n,j,k,a,e,eta,i,ci,G,f,g)
n2j1 = n-2*j-1;
end
function term = q1q1sst2nkterm(n,j,k,a,e,eta,i,ci,G,f,g)
term = ((n - k) - eta/k*(n - k))*k/(n-k);
end
function term = q1q1sst3func(n,j,k,a,e,eta,i,ci,G,f,g)
term = (k-1);
end
function n2j1 = n2jn2jfunc(n,j,k,a,e,eta,i,ci,G,f,g)
n2j1 = (n-2*j)^2;
end
function [W2W3,W2W3k1bye,W2W3k2bye] = getW2W3F(func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,divsi)
ci = cos(i);
% outer j loop
sumj = 0; sumjk1 = 0; sumjk2 = 0;
for j = 0:floor(n/2)
if divsi == true
beta = getBetaSP(j,n,i);
else
beta = getBeta(j,n,i);
end
% inner k loop
sumk = 0; sumkk1 = 0; sumkk2 = 0;
for k = 0:(n-1)
alp = getAlpha(k,n,e);
W3 = getW3(n,j,k,a,e,i,eta,f,g);
sumk = sumk + alp/2^k*W3*func(n,j,k,a,e,eta,i,ci,G,f,g);
if k >= 1
alp1 = getAlpha1(k,n,e);
sumkk1 = sumkk1 + (n-k)/k*alp1/2^k*W3*func(n,j,k,a,e,eta,i,ci,G,f,g);
end
if k >= 2
alp2 = getAlpha2(k,n,e);
sumkk2 = sumkk2 + (n-k)/k*alp2/2^k*W3*func(n,j,k,a,e,eta,i,ci,G,f,g);
end
end
sumj = sumj + beta*sumk;
sumjk1 = sumjk1 + beta*sumkk1;
sumjk2 = sumjk2 + beta*sumkk2;
end
del = getDeltad(n,Jn,J2,a,eta,mu,Re);
W2W3 = del*sumj;
W2W3k1bye = del*sumjk1;
W2W3k2bye = del*sumjk2;
end
function W2W3F = getW2W3m1F(func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re)
% outer j loop
sumj = 0;
for j = 0:floor((n-2)/2)
betaSP = getBetaSPm1(j,n,i);
% inner k loop
sumk = 0;
for k = 0:(n-1)
alp = getAlpha(k,n,e);
W3 = getW3(n,j,k,a,e,i,eta,f,g);
sumk = sumk + alp/2^k*W3*func(n,j,k,a,e,eta,i,ci,G,f,g);
end
if isinf(betaSP) == 0
sumj = sumj + betaSP*sumk;
elseif sumk ~= 0
disp('Inclination singularity');
end
end
del = getDeltad(n,Jn,J2,a,eta,mu,Re);
W2W3F = del*sumj;
end
function k0dadldadg = k0dadldadgterm(n,j,k,a,e,eta,i,ci,G,f,g)
odd = 0;
if mod(n,2) ~= 0
% odd harmonic
odd = 1;
end
sump = 0;
for p = 0:(floor((n-1)/2)-j)
c = n-2*j-2*p;
gam = getGamma(p,j,n);
if odd ~= 1
sump = sump - gam*sin(c*f+c*g)*c;
else
sump = sump + gam*cos(c*f+c*g)*c;
end
end
k0dadldadg = sump;
end
function q1q1sst4t = q1q1sst4term(n,j,k,a,e,eta,i,ci,G,f,g)
odd = 0;
if mod(n,2) ~= 0
% odd harmonic
odd = 1;
end
sump = 0;
for p = 0:(floor((n-1)/2)-j)
c = n-2*j-2*p;
gam = getGamma(p,j,n);
if odd ~= 1
sump = sump - gam*sin(c*f+c*g)*c;
else
sump = sump + gam*cos(c*f+c*g)*c;
end
end
q1q1sst4t = sump;
end
function k0W2Lt3W3fg = k0W2Lt3W3fgterm(n,j,k,a,e,eta,i,ci,G,f,g)
odd = 0;
if mod(n,2) ~= 0
% odd harmonic
odd = 1;
end
sump = 0;
Lt3 = Lt3func(n,j,k,a,e,eta,i,G,ci);
for p = 0:(floor((n-1)/2)-j)
c = n-2*j-2*p;
gam = getGamma(p,j,n);
if odd ~= 1
sump = sump + gam*cos(c*f+c*g)*c;
else
sump = sump + gam*sin(c*f+c*g)*c;
end
end
k0W2Lt3W3fg = sump*Lt3;
end
function dp1spdlgk0term = dp1spdlgk0func(n,j,k,a,e,eta,i,ci,G,f,g)
odd = 0;
if mod(n,2) ~= 0
% odd harmonic
odd = 1;
end
sump = 0;
for p = 0:(floor((n-1)/2)-j)
c = n-2*j-2*p;
gam = getGamma(p,j,n);
if odd ~= 1
sump = sump + gam*cos(c*f+c*g);
else
sump = sump + gam*sin(c*f+c*g);
end
end
dp1spdlgk0term = sump*(n-2*j);
end
function dp1spdlg2k0term = dp1spdlg2k0func(n,j,k,a,e,eta,i,ci,G,f,g)
odd = 0;
if mod(n,2) ~= 0
% odd harmonic
odd = 1;
end
sump = 0;
for p = 0:(floor((n-1)/2)-j)
c = n-2*j-2*p;
gam = getGamma(p,j,n);
if odd ~= 1
sump = sump + gam*sin(c*f+c*g)*c;
else
sump = sump - gam*cos(c*f+c*g)*c;
end
end
dp1spdlg2k0term = sump;
end
function W2k0F = getW2k0F(func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re)
ci = cos(i);
% outer j loop
sumj = 0;
for j = 0:floor(n/2)
beta = getBeta(j,n,i);
sumk = func(n,j,0,a,e,eta,i,ci,G,f,g);
sumj = sumj + beta*sumk;
end
del = getDeltad(n,Jn,J2,a,eta,mu,Re);
W2k0F = del*sumj;
end
function W2kF = getW2kF(func,n,k,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re)
ci = cos(i);
% outer j loop
sumj = 0;
for j = 0:floor(n/2)
beta = getBeta(j,n,i);
sumk = func(n,j,k,a,e,eta,i,ci,G,f,g);
sumj = sumj + beta*sumk;
end
del = getDeltad(n,Jn,J2,a,eta,mu,Re);
W2kF = del*sumj;
end
function [W2W3fg,W2W3fgk1bye,W2W3fgk2bye] = getW2W3fg(func,n,Jn,J2,a,e,eta,i,f,l,G,g,mu,Re,divsi)
ci = cos(i);
% outer j loop
sumj = 0; sumjk1 = 0; sumjk2 = 0;