...1994)

A z_k resonance is a resonant combination of the form k(g-g₆)+s-s₆.

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... of 3131 particles

101 initial values of a in the range 2.1-2.5, and 31 initial values of e, between 0-0.3, with the other elements the same as Vesta's.

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... resonance

We should point out that our assumption of zero obliquities may not be that naive. Studies of Capek & Vokrouhlicky (2004) show that when thermal conductivity is considered, asteroids do tend to evolve towards zero obliquities (and progressively slower or faster spins rates).

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... interval

The proper semimajor axis was computed by averaging the filtered elements over 10 Myr. The synthetic eccentricity and inclination were determined analyzing the equinoctial elements ( $e~\cos~{\varpi}, e~\sin~{\varpi}; \sin~{\frac{I}{2}}~\cos~{\Omega}, \sin~{\frac{I}{2}}~\sin~{\Omega}$) with FMFT. The amplitudes associated with the largest frequencies were the synthetic proper e and i.

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