and exchange of planetary orbital energy and angular momentum using filtered Delaunay elements L， G， H. G and H are equivalent to the planetary orbital angular momentum and its vertical component per unit mass. L is related to the planetary orbital energy E per unit mass as E=μ2/2L2. If the system is completely linear， the orbital energy and the angular momentum in each frequency bin must be constant. Non-linearity in the planetary system can cause an exchange of energy and angular momentum in the frequency domain. The amplitude of the lowest-frequency oscillation should increase if the system is unstable and breaks down gradually. However， such a symptom of instability is not prominent in our long-term integrations.
In Fig. 7， the total orbital energy and angular momentum of the four inner planets and all nine planets are shown for integration N+2. The upper three panels show the long-periodic variation of total energy (denoted asE- E0)， total angular momentum ( G- G0)， and the vertical component ( H- H0) of the inner four planets calculated from the low-pass filtered Delaunay elements.E0， G0， H0 denote the initial values of each quantity. The absolute difference from the initial values is plotted in the panels. The lower three panels in each figure showE-E0，G-G0 andH-H0 of the total of nine planets. The fluctuation shown in the lower panels is virtually entirely a result of the massive jovian planets.
Comparing the variations of energy and angular momentum of the inner four planets and all nine planets， it is apparent that the amplitudes of those of the inner planets are much smaller than those of all nine planets: the amplitudes of the outer five planets are much larger than those of the inner planets. This does not mean that the inner terrestrial planetary subsystem is more stable than the outer one: this is simply a result of the relative smallness of the masses of the four terrestrial planets compared with those of the outer jovian planets. Anoth