Low frequency Delaunay variables

Absolute difference in orbital energy m*(E-E_0), angular momentum m*(G-G_0), and its vertical component m*(H-H_0) calculated by the low-pass filtered orbital elements of each planet in each of our numerical integrations. $m$ is the mass of each planet. Here, the total $E$ is calculated from a Delauney element L as E = -sqr(mu)/2sqr(L). The unit of m*(E-E_0) is 10^(-12)*Msun*AU^2/day^(-2), and that of m*(G-G_0), m*(H-H_0) is 10^(-12)*Msun*AU^2/day^(-1), where Msun is the Sun's mass.

N+1

m*(E-E_0) m*(G-G_0) m*(H-H_0)

N+2

m*(E-E_0) m*(G-G_0) m*(H-H_0)

N+3

m*(E-E_0) m*(G-G_0) m*(H-H_0)

N-1

m*(E-E_0) m*(G-G_0) m*(H-H_0)

N-2

m*(E-E_0) m*(G-G_0) m*(H-H_0)

N-3

m*(E-E_0) m*(G-G_0) m*(H-H_0)

50G+

m*(E-E_0) m*(G-G_0) m*(H-H_0)

50G-

m*(E-E_0) m*(G-G_0) m*(H-H_0)