Browsing by Author "Efroimsky, Michael"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item Complex rotation with internal dissipation. Applications to cosmic-dust alignment and to wobbling comets and asteroids(2002-08) Efroimsky, Michael; Lazarian, Alex; Sidorenko, VladislavNeutron 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 year- or 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.Item Equations for the Keplerian elements: Hidden symmetry as an unexpected source of numerical error(2002-02) Efroimsky, MichaelWe revisit the Lagrange's system of equations for the six osculating elements, in the context of long-term planetary-orbit integration. An accurate re-examination of the derivation of Lagrange's system shows that, in fact, the orbit is always located not in the 6-dimensional space of the osculating elements, but in a certain 3-dimensional submanifold. If an analytic solution to Lagrange's system were available, it would obey this demand. However, whatever numerical integrator will cause drift away from this submanifold. This will result in a new type of accumulating numerical error that will be especially significant at long time spans. We point out an adjustment to be instilled in the integrator, that would eliminate this error. We point out that the choice of the said submanifold is mathematically equivalent to fixing a gauge in field theory. The existing freedom of subminifold choice (~=~freedom of gauge fixing) reveals a symmetry (and a fibre bundle structure) hiding behind Lagrange's system. Just as a choice of the convenient gauge simplifies calculations in electrodynamics, the freedom in choice of the submanifold may, potentially, lead to simpler schemes of orbit integration.Item Euler, Jacobi, and missions to comets and asteroid(2001-07) Efroimsky, MichaelWhenever a freely spinning body is found in a complex rotational state, this means that either the body experienced some interaction within its relaxation-time span, or that it was recently "prepared'' in a non-principal state. Both options are encountered in astronomy where a wobbling rotator is either a recent victim of an impact or a tidal interaction, or is a fragment of a disrupted progenitor. Another factor (relevant for comets) is outgassing. By now, the optical and radar observational programmes have disclosed that complex rotation is hardly a rare phenomenon among the small bodies. Due to impacts, tidal forces and outgassing, the asteroidal and cometary precession must be a generic phenomenon: while some rotators are in the state of visible tumbling, a much larger amount of objects must be performing narrow-cone precession not so easily observable from the Earth. The internal dissipation in a freely precessing top leads to relaxation (gradual damping of the precession) and sometimes to spontaneous changes in the rotation axis. Recently developed theory of dissipative precession of a rigid body reveals that this is a highly nonlinear process: while the body is precessing at an angular rate , the precession-caused stresses and strains in the body contain components oscillating at other frequencies. Dependent upon the spin state, those frequencies may be higher or, most remarkably, lower than the precession rate. In many states dissipation at the harmonics is comparable to or even exceeds that at the principal frequency. For this and other reasons, in many spin states the damping of asteroidal and cometary wobble happens faster, by several orders, than believed previously. This makes it possible to measure the precession-damping rate. The narrowing of the precession cone through the period of about a year can be registered by the currently available spacecraft-based observational means. We propose an appropriate observational scheme that could be accomplished by comet and asteroid-aimed missions. Improved understanding of damping of excited rotation will directly enhance understanding of the current distribution of small-body spin states. It also will constrain the structure and composition of excited rotators. However, in the near-separatrix spin states a precessing rotator can considerably slow down its relaxation. This lingering effect is similar to the one discovered in 1968 by Russian spacecraft engineers who studied free wobble of a tank with viscous fuel.Item Mechanical alignment of suprathermal paramagnetic cosmic-dust granules: the cross-section mechanism(2002-02) Efroimsky, MichaelWe develop a comprehensive quantitative description of the cross-section mechanism discovered several years ago by Lazarian. This is one of the processes that determine grain orientation in clouds of suprathermal cosmic dust. The cross-section mechanism manifests itself when an ensemble of suprathermal paramagnetic granules is placed in a magnetic field and is subject to ultrasonic gas bombardment. The mechanism yields dust alignment whose efficiency depends upon two factors: the geometric shape of the granules, and the angle between the magnetic line and the gas flow. We calculate the quantitative measure of this alignment, and study its dependence upon the said factors. It turns out that, irrelevant of the grain shape, the action of a flux does not lead to alignment if = arccos (1/3).Item The method of variation of constants and multiple time scales in orbital mechanics(2002-11) Newman, William I.; Efroimsky, MichaelThe method of variation of constants is an important tool used to solve systems of ordinary differential equations, and was invented by Euler and Lagrange to solve a problem in orbital mechanics. This methodology assumes that certain ``constants'' associated with a homogeneous problem will vary in time in response to an external force. It also introduces one or more constraint equations motivated by the nature of the time-dependent driver. We show that these constraints can be generalized, in analogy to gauge theories in physics, and that different constraints can offer conceptual advances and methodological benefits to the solution of the underlying problem. Examples are given from linear ordinary differential equation theory and from orbital mechanics. However, a slow driving force in the presence of multiple time scales contained in the underlying (homogeneous) problem nevertheless requires special care, and this has strong implications to the analytic and numerical solutions of problems ranging from celestial mechanics to molecular dynamics.