Libration (molecule)

Abstract: Thirty infrared absorption lines in beryl between 1500 and 11 000 cm−1 are assigned to vibrations of two types of water and to CO2 all in the axial voids of the structure. The spectrum of Type‐I water arises from molecules which are capable of libration and are located between the silicate rings which make up the crystal. The spectrum of Type‐II water arises from molecules in the same sites, but with alkali ions nearby. These molecules are also capable of libration, but at a higher frequency. The Type‐I molecules have their C2 symmetry axes perpendicular to the crystal C6 axis, while the Type‐II molecules have their symmetry axes aligned parallel to the crystal C6 axis. The CO2 molecules are oriented with their long axes prependicular to the crystal C6 axis. Modification of the spectra by heat and hydrothermal treatments was not feasible and the identity of the alkali ions apparently does not influence Type‐II spectrum.

Abstract: Three-dimensional orbits in the vicinity of the interior libration point (Li) of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planned for the 1990s. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. The primary goal of this effort is the development of a Stationkeeping strategy applicable to such trajectories. A method is presented that uses maneuvers executed (impulsively) at discrete time intervals. The analysis includes some investigation of a number of the problem parameters that affect the overall maneuver costs. Simulations are designed to provide representative station- keeping costs for a spacecraft moving in a libration point trajectory, and preliminary results are summarized. RAJECTORY planning for a number of scientific mis- sions scheduled for launch in the 1990s includes the possi- ble use of three-dimensi onal halo or Lissajous orbits in the vicinity of the interior L! libration point of the Sun-Earth/ Moon barycenter system.1 This effort is directed toward the development of a Stationkeeping strategy that can be used to maintain spacecraft near such nominal libration point trajec- tories. A significant number of analyses have been completed that involve Stationkeeping methods for Earth orbiting satel- lites; maintaining a spacecraft on a libration point orbit, how- ever, has received limited attention. In the late 1960s, Far- quhar2 developed a number of possible Stationkeeping strat- egies for libration point orbits. Later, in 1974, a station- keeping method for spacecraft moving on halo orbits in the vicinity of the Earth-Moon translunar libration point L2 was published by Breakwell et al. 3 In contrast, specific mission requirements influenced the design of the Stationkeeping strat- egy for the first libration point mission. When the Interna- tional Sun-Earth Explorer-3 (ISEE-3) satellite was injected into a halo orbit associated with the interior L! libration point of the Sun-Earth system in 1978, a series of maneuvers exe- cuted at approximately three-month intervals was used for Stationkeeping.4 More recently, a series of papers have pre- sented results from studies that use Floquet and invariant manifold theories to develop a ''loose" Stationkeeping strat- egy for halo-type orbits.5"8 Similar to ISEE-3, the method also uses discrete maneuvers, applied at varying time intervals, that control the trajectory near the nominal path. A significant goal of this study is the development of a potentially ''tight" control strategy for Stationkeeping that can be applied to both halo and Lissajous trajectories (as well as other possible types of libration point paths). In this approach, the allowable deviation of the actual trajectory relative to the nominal path can be varied over a wide range depending on mission require- ments. Of course, low costs are desirable as well.

Abstract: Simulation of the dynamics of an electrodynamic tether on a circular inclined orbit shows a very complex motion driven by the electrodynamic forces acting on the conductive tether. These forces depend on the current flowing in the wire, the Earth magnetic field, the orbital velocity and the tether position. In this paper we use a simple model to describe the dynamic effects of these forces. The tether is modeled as a rigid rod with point masses at the ends. We also adopt a non-tilted dipole model for the Earth magnetic field, and we assume that the tether current is constant. When the current is null, the system has a stable equilibrium position with the tether aligned along the local vertical. When the current is different from zero, a periodic motion appears. A nonlinear analysis of the motion shows that the periodic solutions are always unstable (within the limitation of the model considered in the paper). The physical reason for the instability is that the electrodynamic forces pump energy continually into the system. The net energy increase per orbit for the periodic solution (or state space trajectory) is zero. However, any nonperiodic trajectory in its neighborhood has a positive net energy flux per orbit so that after several orbits the in-plane libration becomes a rotation. The mechanism responsible for this instability depends on the orbital inclination. Unlike other destabilizing mechanisms found in electrodynamic tethers, this one is present in any kind of tether system with either a flexible or a rigid tether, operating in the generator or thruster mode and utilizing a bare tether or a large spherical termination to collect the ionospheric electrons. The instability described in this paper is independent of the presence of resonant force components that may be generated by the magnetic and plasma fields.

Abstract: Introduction M of a spacecraft presents two dynamical aspects of interest. The most obvious one is the trajectory traced by its center of mass which is governed by the classical Keplerian relations. However, spacecraft are not point masses as Kepler assumed in the analysis of planetary bodies. They have finite size and hence inertia. Thus a satellite, while negotiating a trajectory, may execute rotational motion about its center of mass, commonly referred to as libration.