Three-dimensional nonlinear stability analysis of the sun-perturbed earth-moon equilateral points.
Nonlinear analysis of earth-moon system motion stability in three dimensions near L4 libration point when perturbed by sun
SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Nonlinear analysis of earth-moon system motion stability in three dimensions near L4 libration point when perturbed by sun
Energy and motion equations for libration of lunar satellite
Here, we present a neutron vibrational spectroscopy study to investigate the influence of NH$^+_4$ motion on the magnetism in [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)]. The parent compounds, (NH 4 ) 2 [FeCl 5 (H 2 O)] (x = 0) and K 2 [FeCl 5 (H 2 O)](x = 1) are isostructural at room temperature, yet displaying drastically different magnetic and multiferroic behavior. K 2 [FeCl 5 (H 2 O)] is nonmultiferroic with type-A collinear antiferromagnetic structure below T N ≈ 14.06 K, whereas (NH 4 ) 2 [FeCl 5 (H 2 O)] is a type-II multiferroic with incommensurate cycloidal spin structure below T FE ≈ 6.8 K. A recent study of the dielectric, structure, and magnetic properties in the mixed [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)] shows that a small amount of potassium substitution to replace NH$^+_4$ transforms the spin structure from incommensurate cycloidal (x ≤ 0.06) into commensurate collinear antiferromagnetic (x ≥ 0.15), indicating NH$^+_4$ is essential to the emergent phenomena observed in this molecular multiferroic compound. Our vibrational spectroscopy study reveals that NH$^+_4$ libration and torsion motion exhibit substantial temperature dependence at low temperatures. The intensity of NH$^+_4$ libration and torsion modes increases slightly at 5 K in comparison with data at 25 K behaving like a magnon, indicating that they are coupled to the magnetism in (NH 4 ) 2 [FeCl 5 (H 2 O)]. Comparing data of x=0, 0.06, 0.09, and 0.15 samples further illustrates that the strength of the increased signal in NH$^+_4$ libration mode is very sensitive to potassium concentration. The signal diminishes quickly with increasing potassium concentration and vanishes in the x = 0.15 sample corresponding to the magnetic structure change for x ≥ 0.15. The results directly link the anomalous behavior in NH$^+_4$ libration motion to the magnetism in [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)], providing new insights into the crucial role NH$^+_4$ plays in the coupled phenomena in (NH 4 ) 2 [FeCl 5 (H 2 O)]. The unique information opens a new door to go through in searching for new multifunctional materials by incorporation of NH 4 via a material-by-design approach.
Restricted three-body problem for motion analysis of planetoid orbiting around triangular equilibrium point
Motion of passively damped gravity-stabilized artificial satellite tumbling or rotating about arbitrary axis
An expression for the strength of the synchronous rotation of the moon in terms of upper and lower limits on the rotational period is derived. The rotational periods for locked-in motion are expected to lie between 1.025T and 0.975T, where T is the period of revolution.
Particle motion near triangular libration point in Earth-Moon system
Lagrange-Laplace theory of lunar physical librations extended to include reduced estimate of mechanical ellipticity of lunar equator
Lunar gravity field and physical librations of moon
Derivation of explicit equations governing deformations of self-gravitating viscous bodies in external force field for application to physical librations of moon
Cassini second and third laws of lunar rotation are independent of first one
Structural and librational dynamics of satellite deploying flexible booms or antennas
Periodic solutions of elliptical and restricted four-body problems about libration points of restricted three-body problem
Stability analysis of long period Trojan librations treated as short period oscillations about long period reference solution
Oscillating libration orbits with period rigorously commensurable in rational fraction to basic long period
Librational and flexural resonances induced in satellite whose center of mass is moving in planar elliptic orbit
Nonlinear resonance effect on attitude librations of undamped rigid gravity gradient stabilized satellite in circular Earth orbit