Vibrational stabilization by an internal binary: a negative result

We test whether a tight central binary can stabilize, by analogy with the Kapitza pendulum, an equilateral triangle of three equal masses that is unstable with a single central mass. We compare the survival time with that of a control group with the same total mass concentrated in a single body, for three central masses, ten binary separations, and both senses of rotation, and we repeat the test at the Routh stability boundary of the Lagrange triangle. In no case did the binary significantly prolong survival; for larger separations, it shortened survival to about 8% of the control. A scaling estimate explains the result: since Kepler's third law links the amplitude and frequency of the quadrupole excitation, the effective Kapitza term decays with the seventh power of the binary separation. Passive vibrational stabilization does not occur in this system.