Complex rotation with internal dissipation. Applications to cosmic-dust alignment and to wobbling comets and asteroids

Neutron stars, asteroids, comets, cosmic-dust granules, spacecraft, as well as whatever other freely spinning body dissipate energy when they rotate about any axis different from principal. We discuss the internal-dissipation-caused relaxation of a freely precessing rotator towards its minimal-energy mode (mode that corresponds to the spin about the maximal-inertia axis). We show that this simple system contains in itself some quite unexpected physics. While the body nutates at some rate, the internal stresses and strains within the body oscillate at frequencies both higher and (what is especially surprising) lower than this rate. The internal dissipation takes place not so much at the frequency of nutation but rather at the second and higher harmonics. In other words, this mechanical system provides an example of an extreme non-linerity. Issues like chaos and separatrix also come into play. The earlier estimates, that ignored non-linearity, considerably underestimated the efficiency of the internal relaxation of wobbling asteroids and comets. At the same time, owing to the non-linearlity of inelastic relaxation, small-angle nutations can persist for very long time spans. The latter circumstance is important for the analysis and interpretation of NEAR’s data on Eros’ rotation state. Regarding the comets, estimates show that the currently available angular resolution of spacecraft-based instruments makes it possible to observe wobble damping within yearor maybe even month-long spans of time. Our review also covers pertinent topics from the cosmic-dust astrophysics; in particular, the role played by precession damping in the dust alignment. We show that this damping provides coupling of the grain’s rotational and vibrational degrees of freedom; this entails occasional flipping of dust grains due to thermal fluctuations. During such a flip, grain preserves its angular momentum, but the direction of torques arising from H2 formation reverses. As a result, flipping grain will not rotate fast in spite of the action of uncompensated H2 formation torques. The grains get “thermally trapped,” and their alignment is marginal. Inelastic relaxation competes with the nuclear and Barnett relaxations, so we define the range of sizes for which the inelastic relaxation dominates. Subject headings: Euler equations, elliptic functions of Jacobi, celestial mechanics, inelastic relaxation, inelastic dissipation, nonlinear dynamics, interstellar medium (ISM), cosmic dust, comets, asteroids, Eros. PACS: 96.50.Gn, 96.30.Ys, 96.35.Cp, 96.35.Fs, 05.45.-a, 45.40.-f, 95.10.Ce, 95.10.Fh, 45.50.Pk, 98.38.Cp, 98.58.Ca