Elements of a theory of librational motions in the elliptical restricted problem.
Nonperiodic librational motions in restricted three-body problem for relatively elliptic motion of two finite masses
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Nonperiodic librational motions in restricted three-body problem for relatively elliptic motion of two finite masses
Librational motion analysis for elliptical restricted three-body problem
Spacecraft libration point motion in restricted four body model including earth-moon orbit plane inclination to ecliptic, noting solar effects
The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.
The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.
In contrast to the common viewpoint that bacteriochlorophyll (BChl) motion is largely absent within the chlorosome assembly, physics-based modeling points to a crucial role of the nanoscale librational motion of the macrocycle for the transfer of excitons. To elucidate this motion experimentally, compositional uniformity and high sensitivity are required. We focused on uniformly 13 C labeled chlorosome preparations from the bchQ mutant Chlorobaculum tepidum with significantly enhanced structural homogeneity. The librational motion is characterized using Rotational Echo DOuble Resonance (REDOR), and in addition, the impact of temperature on specific functionalities within BChl molecules is studied with 1-dimensional and 2-dimensional dipolar and scalar-based MAS NMR measurements. Results show the gradual freezing of the tails and side chains of the BChls with decreasing temperature. However, the librational motion analyzed by measuring the 5C–H dipolar coupling strength obtained from REDOR data sets persists at different temperatures. REDOR simulations show a close match to the experimental dephasing frequency of oscillation for a dipolar coupling strength of 17.5 ± 0.5 kHz which is considerably less than the dipolar coupling strength of 22.7 kHz in the rigid limit. Following a two-site jump model, we arrive at an estimate for BChl libration sampling at an angle of θ = 48 ± 4°, corroborating that the macrocycle indeed experiences significant librational motion on a time scale that is short compared to the NMR measurement time. This finding is in full quantitative support of the dominant rotational motion exhibited by the BChl macrocycle estimated from early MD simulations.
Long period of nonperiodic librational motion about equilateral points of restricted three-body problem
Material elasticity effects on planar librational motion of rigid satellite under action of gravity gradients
Material elasticity effects on planar librational motion of rigid satellite under action of gravity gradients
Mathematical model for lunar librational motion
Librational motion of gravitationally oriented rigid satellite in elliptic orbit studied by canonical transformation
Far IR spectra and space group of crystalline hydrazine and hydrazine-d4 noting coupling of translational and librational motions
Applied mathematics in celestial mechanics - theory of librational motions, earth shape, and satellite orbit calculations
Numerical solutions for librational motion of Mercury obtained by applying Runge-Kutta integration
Here, we present an experimental and theoretical study of the interplay between ultrafast electron dynamics and librational dynamics in liquid nitrobenzene. A femtosecond ultraviolet pulse and two femtosecond near-infrared pulses interact with nitrobenzene molecules, generating a four-wave mixing nonlinear signal measured in the Optical Kerr Effect geometry. The signal is measured to be nonzero only at negative time delays, corresponding to the near-infrared pulses arriving before the ultraviolet pulse. We perform time-dependent Quantum Master Equation calculations with classical libration to simulate the experiment. The simulations support the conclusion that the near-infrared pulses launch librational motion while creating electronic coherences resulting in a libration-modulated electronic nonlinear response. The analysis of the phase-matched four-wave mixing signals suggests a nonparametric process leaving the molecules in an excited electronic state, providing new insight into ultrafast nonlinear optical interactions in liquids and advancing toward probing ultrafast electronic coherences in complex molecular liquids.
Numerical analysis of librational motion of particle around lagrangian triangular point in semirestricted three-body problem
A simplified model of the strong atmospheric perturbation of a small satellite attached to the orbiter by a long, rigid tether predicts undesirable uncontrolled libration motions similar to those from sophisticated models. The simplified model is used to compare performance limitations of two simple control systems that rely only on tether tension for three-dimensional control. Because the effects on libration of both the changing kinematic and atmospheric drag torques caused by changing length are largely predictable, the controller that models these changes has substantially better performance. In particular, the altitude variation of the tethered satellite above an oblate earth can be controlled substantially better with a controller that uses a length command adapted to these predictable changes than one that only reacts to tension changes. Also, small amplitude out-of-plane librations, that are coupled only to second-order with changing length, can be damped substantially faster by the controller that periodically commands properly phased length changes than by the controller that only reacts to the second-order changes in tension.
Methylamine crystals lattice vibrations IR spectra recordings, making spectral band assignments according to translational and librational motions