The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations

This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics and presents some new results. As is well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this reduction is offered by the underlying symmetry, which stems from conservation of the angular momentum and rotational kinetic energy. When a perturbation is turned on, these quantities are no longer preserved. Nonetheless, the language of reduced description remains extremely instrumental even in the perturbed case. We describe the canonical reduction performed by the Serret-Andoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specifically, we consider the case of angular-velocity-dependent torques, and discuss the variation-of-parameters-inherent antinomy between canonicity and osculation. Finally, we address the transformation of the Andoyer variables into the action-angle ones, using the method of Sadov

Multifactorial Method of Search for Small Bodies in Close Orbits

© 2020, Pleiades Publishing, Ltd. Abstract: The results of the search for Apollo, Amor, and Aten asteroids with the orbits close to those of meteoroids of the δ-Cancrids meteor complex (code DCA), which consists of the northern (code NCC) and southern (code SCC) branches, are presented. The search for small bodies in close orbits was performed on the basis of a multifactorial method of combining several criteria: Drummond orbital similarity criterion, Kholshevnikov metric, and parameters of the dynamic evolution of the orbits using two catalogs of meteor orbits (Japan Meteor Society, SonatoCo, and CAMS Meteoroid Orbit Database v2.0, CAMS) obtained from television observations. Asteroids in close orbits with the meteoroid orbits of the northern NCC and southern SCC branches of the δ-Cancrids are identified only in the Apollo group. The following asteroids are common for the NCC and SCC branches: 2015 PU228, 2014 YQ34, 2017 YO4 (according to the CAMS orbit catalog); Hephaistos 1978 SB, 2003 RW11, 2006 BF56, 2011 SR12, 2014 RS17, 2001 YB5 (SonatoCo catalog). The asteroid 85182 (1991 AQ) is identified only with the northern NCC branch but in two catalogs of meteor orbits

Impact-generated dust clouds around planetary satellites: spherically symmetric case

An analytic model of an impact-generated, steady-state, spherically symmetric dust cloud around an atmosphereless planetary satellite (or planet-Mercury, Pluto) is constructed. The projectiles are assumed to be interplanetary micrometeoroids. The model provides the expected mass, density, and velocity distributions of dust in the vicinities of parent bodies. Applications are made to Jupiter's moon Ganymede and six outer satellites of Saturn. In the former case, the model is shown to be consistent with the measurements of the dust detector system onboard the Galileo spacecraft. In the latter case, estimates are given and recommendations are made for the planned experiment with the Cassini cosmic dust analyzer (CDA) during targeted flybys of the spacecraft with the moons. The best CDA pointing to maximize the number of detections is in the ram direction. With this pointing, measurements are possible within a few to about 20min from the closest approach, with maximum minute impact rates ranging from about 1 for Phoebe and Hyperion to thousands for Enceladus. Detections of the ejecta clouds will still be likely if CDA's angular offset from the ram direction does not exceed /45°. The same model can be applied to dust measurements by other space missions, like New Horizons to Pluto or BepiColombo to Mercury