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Planetary orbital elements
For example, today’s date and current time of loading this page is the Julian time Note that you also need the universal time (UT). For us that’s local time plus 5 hrs. Convert this to UT in the formula above
Nonlinear equations of motion: Poincare-Lindstedt method
operator x; depend x,!T; w:=w0+b*w1+b^2*w2; y:=for n:=0:2 sum b^n*x(n); eqtn:=df(y,!T,2)+w^2*y+b*(y^2-1)*df(y,!T); eq0:=coeffn(eqtn,b,0); eq1:=coeffn(eqtn,b,1); eq2:=coeffn(eqtn,b,2); let x(0)=!A*cos(w0*!T); eq1; for all z let cos(z)^2=(1+cos(2*z))/2; for all z,q let cos(q)*sin(z)=(sin(q+z)-sin(q-z))/2; eq1; let w1=0; let !A=2; eq1; let x(1)=-(1/(4*w0))*sin(3*w0*!T); for all z,q let sin(z)*sin(q)=(cos(z-q)-cos(z+q))/2; for