Large amplitude bending vibrations of the triatomic molecule: Low angular momentum states

1986 ◽  
Vol 84 (3) ◽  
pp. 1565-1573 ◽  
Author(s):  
Martin L. Sage
Keyword(s):  
Angular Momentum ◽  
Large Amplitude ◽  
Triatomic Molecule ◽  
Bending Vibrations

Periodic Orbits of Radially Symmetric Systems with a Singularity: the Repulsive Case

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Periodic Forcing ◽  
The Third ◽  
Large Angular Momentum ◽  
Symmetric Systems

AbstractWe study radially symmetric systems with a singularity of repulsive type. In the presence of a radially symmetric periodic forcing, we show the existence of three distinct families of subharmonic solutions: One oscillates radially, one rotates around the origin with small angular momentum, and the third one with both large angular momentum and large amplitude. The proofs are carried out by the use of topological degree theory.

Large Amplitude Hamiltonian of a Triatomic Molecule

1977 ◽  
Vol 32 (12) ◽  
pp. 1450-1456 ◽  
Author(s):  
R. Wallace ◽  
Ch. V. S. Ramachandra Rao
Keyword(s):  
Ground State ◽  
Large Amplitude ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Curvilinear Coordinates ◽  
Large Displacements ◽  
Triatomic Molecule ◽  
Quadratic Potential ◽  
Method Of Calculation ◽  
Vibrational Energy Levels

Abstract An expression for the Hamiltonian H(ρ1, ρ2, ρ3) of a vibrating-rotating triatomic molecule is derived using three curvilinear coordinates gi, Q 3 in such a way that the Hamiltonian obtained is applicable to any bent triatomic molecule and allows for large displacements in all the three modes of motion. A variational technique is then used to calculate the low lying vibrational energy levels (υ1, υ2, υ3) of the H2O molecule in its X̃1A1 ground state. The kinetic energy of the Hamiltonian T(ρ1, ρ2, ρ3) takes into account the large amplitude character of the three modes together with their interaction. But in order to minimize the formidable amount of computation, a simple quadratic potential F(ρ1, ρ2, ρ3) is assumed for all the three modes which only serves to illustrate the method of calculation.

scholarly journals Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Shengjun Li ◽  
Yuming Zhu
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
The Other ◽  
Topological Degree Theory ◽  
Families Of Periodic Orbits ◽  
Large Angular Momentum

We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude.

scholarly journals Revisit of rotational dynamics of Asteroid 4179 Toutatis from Chang'e-2's flyby

2015 ◽  
Vol 10 (S318) ◽  
pp. 156-159
Author(s):  
Yuhui Zhao ◽  
Shoucun Hu ◽  
Jianghui Ji
Keyword(s):  
Angular Momentum ◽  
Fourier Analysis ◽  
Large Amplitude ◽  
Large Deviation ◽  
Rotational Dynamics ◽  
Euler Angles ◽  
Rotational Axis ◽  
Angular Momentum Vector ◽  
Shape Model ◽  
Momentum Vector

AbstractThis paper presents analysis of the rotational parameters of Toutatis based on the observational results from Chang'e-2's close flyby. The 3-D shape model derived from ground-based radar observation is used to calculate the 3-1-3 Euler angles at the flyby epoch, which are evaluated to be −20.1° ± 1°, 27.6° ± 1° and 42.2° ± 1°. The large amplitude of Toutatis' tumbling attitude is demonstrated to be the result of the large deviation of the angular momentum axis and the rotational axis. Two rotational periods are evaluated to be 5.38±0.03 days for rotation about the long axis and 7.40±0.03 days for precession of the long axis about the angular momentum vector based on Fourier analysis. These results provide a further understanding of rotational state of Toutatis.

scholarly journals On the relationship between molecular spectroscopy and statistical mechanics: Calculation of partition functions for triatomic molecules undergoing large-amplitude bending vibrations

2011 ◽  
Vol 76 (4) ◽  
pp. 539-555 ◽  
Author(s):  
Milan Sencanski ◽  
Jelena Radic-Peric ◽  
Miljenko Peric
Keyword(s):  
Molecular Structure ◽  
Ab Initio Calculations ◽  
Structure Data ◽  
Large Amplitude ◽  
Molecular Spectroscopy ◽  
Energy Levels ◽  
Partition Functions ◽  
Bending Vibrations ◽  
Triatomic Molecules ◽  
The Relationship

The evaluation of partition functions for triatomic molecules undergoing large-amplitude bending vibrations is discussed. It was supposed that the needed molecular structure data were obtained by means of ab initio calculations. Special attention is paid to the coupling between the bending and stretching modes and the interplay between bending motions and rotations. An appropriate scheme for variational computation of the energy levels is developed.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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