Principal Axes Of Inertia Research Articles

Internal and external force fields and normal vibrations of the water molecules in Ba(ClO 3) 2.H 2O and K 2C 2O 4.H 2O

Normal coordinate analyses of the water molecules in Ba(ClO 3) 2.H 2O and K 2C 2O 4.H 2O have been made. The water molecules have been allowed to vibrate in an effective force field from stationary surrounding atoms, resulting in nine normal modes. Vibrational data from earlier infrared, Raman and neutron inelastic scattering studies have been used for the determination of the force constants. The OH stretching force constants are 7.80 and 6.97 mdyn Å −1 for the water molecules in Ba(ClO 3) 2.H 2O and K 2C 2O 4.H 2O, respectively. The force constants for the rotational vibrations about the principal inertial axes of the water molecules range from 0.052 to 0.48 mdyn Å rad −2 and those for the translational vibrations along these axes from 0.17 to 0.66 mdyn Å −1.

13C nuclear spin-lattice relaxation study of anisotropic solvent rotational diffusion in the polystyrene/ trans-decalin system

The rotational diffusion tensor for the solvent trans-decalin has been determined as a function of temperature (21°–55°C) and polystyrene concentration (0–13% w/w) from 13C spin-lattice relaxation data. The sensitivity of rotational diffusion behaviour of the trans-decalin molecule to changes in solution conditions was found to be essentially proportional to the axial ellipticities of the respective principal rotational axes. The degree of anisotropic motion was found to increase strongly upon increasing the polystyrene concentration and decreasing the temperature. Apparent activation energies for rotation about each of the principal axes of inertia have been calculated for the series of polystyrene concentrations.

The EPR spectrum of the HO 2 radical and determination of ground state parameters

The detection of lines in the gas phase EPR spectrum of the HO 2 radical at a frequency of 9 GHz is reported. The measurements are combined with the data from the far infrared LMR spectrum and with the zero-field frequencies in the microwave spectrum and fitted to determine a very nearly complete set of ground state parameters. A theoretical relationship is used in order to determine all the non-zero components of the spin rotation tensor ϵ in the principal inertial axis system. The spin-rotation interaction is interpreted in terms of the admixture of both the A ̃ 2A′ state and higher 2 A′ states. The three principal components of the electron spin g-tensor are determined by the magnetic resonance data and are found to be well predicted by Curl's relationship from the spin-rotation tensor. In addition, it was found to be necessary to include terms from the rotational Zeeman effect to obtain a satisfactory fit of the data. Two of the principal components of the rotational g-tensor are determined; the valuefor g r aa is shown to be consistent with Coriolis mixing of the A ̃ 2A′ state. The hyperfine parameters determined in the fit of the microwave data are interpreted in terms of a simple molecular orbital description. The results suggest that about 27% of the spin density is on the central O atom.

Effect of a Nonconstant Cma on the Stability of Rolling Aircraft

An analytical study is carried out of the behavior of modern high-speed aircraft of inertially slender configurations in maneuvers involving large rates of roll. Inertia cross-coupling, as well as a linear variation of longitudinal static stability (C/m-alpha/) with angle of attack, are considered. The steady-state solutions of the nonlinear equations of motion, based on principal inertia axes, are studied to obtain useful information on the response behavior of the state variables during roll maneuvers. It is shown that, in addition to the critical values of aileron deflection that have been previously found to limit a steady-state roll with constant longitudinal static stability, there can be two new critical values introduced by a linear decrease of the absolute value of longitudinal static stability with angle of attack. For aileron deflections near these critical values, the response of the aircraft exhibits violent oscillations and dangerous peak loads, due to the cross-coupled motion accompanying a roll maneuver. These critical values define a new range of aileron deflections in which no steady-state roll is possible.

A generalized analysis of the vibration of circular rings

A theory is presented which describes the various inextensional vibrations of a circular ring. The cross-sectional shape of the ring is assumed to be constant around its circumference, but otherwise is unrestricted. In particular, it is not assumed that the principal axes of inertia of the cross-section lie in the ring plane. The theory can predict several distinct types of ring vibration, including flexural, torsional and shear waves. Excellent agreement is found with experimental results obtained from two test rings.

Three-dimensional determination of the center of the Watts datum relative to the lunar center of mass

view Abstract Citations (7) References (2) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Three-dimensional determination of the center of the Watts datum relative to the lunar center of mass. Mulholland, J. D. Abstract The location of the origin of the Watts datum for the marginal zone of the moon is determined using results of 2770 photoelectric occultation observations obtained over an 18-yr period in combination with 1787 laser time-delay measurements carried out over a five-year period. The lunar ephemeris employed is an experimental one developed from a much shorter span of laser observations. The final solution is obtained by adopting LURE2 parameters and correcting 19 lunar orbital, solar orbital, and coordinate-system parameters. The offsets for the center of the Watts datum are found to be approximately +6.8 km for x1, -2.5 km for x2, and +0.06 km for x3 with respect to the lunar principal axes of inertia. Publication: The Astronomical Journal Pub Date: April 1977 DOI: 10.1086/112049 Bibcode: 1977AJ.....82..306M Keywords: Astronomical Models; Lunar Limb; Lunar Occultation; Selenography; Astronomical Photography; Electrophotometers; Ephemerides; Laser Applications; Lunar Orbits; Mathematical Models; Solar Orbits; Stellar Occultation; Time Lag; Astronomy full text sources ADS |

Perturbation Solution for the Flat Spin Recovery of a Dual-§pin Spacecraft

Euler's differential equations for free-body attitude motion are solved for the constant bearing axis torque recovery maneuver of a spacecraft with a symmetric rotor and asymmetric platform. The rotor bearing axis coincides with the spacecraft's centroidal principal axis of least inertia. The recovery time and the residual nutation angle are algebraically related to the initial flat spin rate, the spacecraft inertia properties, and the bearing axis torque. The differential equations are solved by use of two asymptotic parameter expansions of the multiple time scale type, which are matched to a transition expansion with a limit process matching procedure.

ChemInform Abstract: MICROWAVE SPECTRUM AND QUADRUPOLE COUPLING CONSTANTS OF 3‐CHLOROPYRIDINE

Abstract The microwave spectrum of 3-chloropyridine has been observed between 7000 MHz and 18000 MHz. An analysis of the spectrum gave the following values for the rotational constants: A = 5839.53 ± 0.03 MHz, B = 1604.19 ± 0.01 MHz, C = 1258.31 ± 0.01 MHz for C 5 H 4 N 35 Cl and A = 5839.30 ± 0.02 MHz, B = 1558.52 ± 0.01 MHz and C = 1229.96 ± 0.01 MHz for C 5 H 4 N 37 Cl. The inertial defect of 0.050 amu A 2 shows the molecule to be essentially planar. The hyperfine structure on a number of rotational transitions has been measured and analyzed. The three diagonal elements of the nuclear quadrupole coupling tensors in the principal inertial axis systems obtained are:

On the stability of permanent rotation of a heavy solid body about a fixed point: PMM vol. 40, n≗ 3, 1976, pp. 408–416

The permanent rotation of a heavy solid body about its principal axis of inertia with a fixed point is considered. Stability is investigated with the use of the theorem on the stability of Hamiltonian systems with two degrees of freedom in the general elliptic case. It is shown that in the absence of certain resonance relationships in the region of necessary stability conditions, which does not coincide with the region of known sufficient conditions, the first approximation indicates the existence of stability, except possibly, in the case when the parameters of the problem lie on some specific manifolds of the parameter space. Subregions that are free of such exceptional manifolds are indicated in each region of necessary stability conditions. Necessary stability conditions for permanent rotation about principal axes of inertia of a solid body were investigated by Grammel [3]. Sufficient conditions that matched necessary conditions were obtained by Chetaev in the case of Lagrange integrability [4], and by Rumiantsev in that of Kowalewska integrability [5]. Permanent rotation of a body with arbitrary mass distribution about its principal axis of inertia was considered in [6–8], where sufficient stability conditions were established by Chetaev's method and on the basis of the Routh theorem. Bifurcation of permanent rotations and changes of stability were investigated in [9].

Microwave spectrum and quadrupole coupling constants of 3-chloropyridine

The microwave spectrum of 3-chloropyridine has been observed between 7000 MHz and 18000 MHz. An analysis of the spectrum gave the following values for the rotational constants: A = 5839.53 ± 0.03 MHz, B = 1604.19 ± 0.01 MHz, C = 1258.31 ± 0.01 MHz for C 5H 4N 35Cl and A = 5839.30 ± 0.02 MHz, B = 1558.52 ± 0.01 MHz and C = 1229.96 ± 0.01 MHz for C 5H 4N 37Cl. The inertial defect of 0.050 amu Å 2 shows the molecule to be essentially planar. The hyperfine structure on a number of rotational transitions has been measured and analyzed. The three diagonal elements of the nuclear quadrupole coupling tensors in the principal inertial axis systems obtained are: ▪

Vibrations and stability of a free rod of variable mass, taking account of motion of its mass along the axial line

The moving Cartesian coordinate system cuvw is fixed at the center of mass of the rod and its axes are directed along the principal axes of inertia of the instantaneously deformed rod. The curvilinear Lagrangian coordinate x measured from point A along the elastic line toward poin t B is used as an independent variable. The position of the rod at a given instant is determined by the position of its center of mass with respect to the fixed Cartesian system OXYZ, the angle of rotation r of the moving system, and the function V(x, t) which measures the deflection of the axial line in the direction of the v axis of the moving system. These coordinate systems and variables were proposed in [2]. Along the axial line of the rod there is an internal channel in which a stream of ideal fluid moves with a constant velocity u 0 relative to the axes of the natural trihedron fixed with respect to the elastic line of the rod. The stream consists of particles detached from the rod. The detachment of mass into the channel is assumed to take place uniformly over the whole length of the rod. The mass detached from a unit length of the rod per unit time is assumed constant and is denoted by #. Particles of the rod are detached with finite relative velocities equal to the velocity of the stream in the channel. As a result a distributed reactive tractive load is produced. The time varying density of the rod is expressed in terms of the constants m 0 and # by the relation m (t) = mo -- ~t. (1) For the reactive force density we take the expression

On the Critical Speed Regions of an Asymmetric Rotating Shaft Supported by Asymmetrically Elastic : 1st Report, On the Unstable Regions

To make clear the dynamic characteristics of a rotating shaft exactly, we should take into consideration both the asymmetry of a shaft and the elasticity, especially the asymmetric elasticity of supports. The authors considered an idealized model, in which a disk was mounted at the center of a flat shaft with different bending rigidities in two mutually vertical directions corresponding to the principal axes of inertia of the section. The supporting parts of both ends were supported by springs in two vertical directions, as a concentrated masses system, in which masses were concentrated at the central disk part and supporting parts of both ends, and the equations of motion with periodic coefficients were derived in terms of springs. As a first step, analyses were made by the asymptotic method to know what effects would be caused to the unstable regions of this system by the asymmetry of the shaft, the rigidities of the supporting parts and their asymmetry, the internal and external dampings, and others, and in what relation these acted with each other. Some of the results of analyses have been experimentally confirmed.

Molecular Structure, Quadrupole Coupling Tensor and Dipole Moment of Ethyl Cyanide

The microwave spectra of CD3CH2CN, 13CH3CH2CN, CH3 13CH2CN and CH3CH2C15N have been measured. In addition the spectrum of CH3CH2 13CN has been remeasured with greater accuracy. From these spectra and those previously reported - CH3CH2CN, CH3CD2CN, CH2DCH2CN (sym) and CH2DCH2CN (asym) - a complete rs-structure has been calculated by the equations of Kraitchman and Chutjian. r0-structure calculations were performed with different assumptions due to the symmetry of the molecule. A comparison between r0- and rs-structure was made and showed good agreement especially for the atoms of the frame. The quadrupole coupling constants of the above mentioned isotopes of ethyl cyanide were obtained from the hyperfine structure of the spectra with the exception of CH3CH2C15N, which has no nucleus with quadrupole moment. The quadrupole coupling tensor in its principal axis system was determined from the constants of CD3CH2CN and CH3CD2CN using the angle e between their principal axes of inertia in the a-b-plane. From Stark effect measurements the dipole moment of CH3CH2CN was reevaluated. To determine the direction of the dipole moment Stark effect measurements for CD3CH2CN and CH3CD2CN were carried out.

Effects of Asymmetries in the Rotor and Flexible Joint of a Dual-Spin Spacecraft

Most past investigations of dual-spin spacecraft have assumed that the platform and rotor are symmetric and rigidly connected. Recently, Cretcher and Mingori, Wenglarz, Willems, and Bainum have considered the effects of flexibility in different parts of dual-spin spacecraft. Scher and FarrenkopP have considered the effects of an asymmetric rotor rigidly connected to the platform. However, the effects of unsymmetric transverse inertias in a dual-spin spacecraft with a flexible joint have not been published. They have been rigorously investigated in rotors and gyroscopes by Brosens and Crandall and by Foote, Poritsky, and Slade. This paper presents the results of an investigation of these effects on the attitude motion of dual-spin spacecraft. It includes only those cases for which the equations of motion can be transformed into linear equations without periodic coefficients. The model, shown in Fig. 1, consists of a spinning rotor which is connected to a nonspinning platform by a flexible joint. The axes XQYQZQ are fixed m space with the origin at the CM of the system. The axes X2Y2Z2 are the principal inertia axes of the platform and are described with respect to axes X0Y0Z0 by rotations 9X about the X0 axis and 0y about the Y1 axis. The orientations of X4Y4Z4, where Z4 is the drive axis of the rotor, are described by rotations x about the X2 axis and y about the Y3 axis. Axes X^ Y4Z4, which will be the principal inertia axes for a balanced rotor, are fixed in the rotor and rotating at the spin rate about the Z4 axis. For an unbalanced rotor, the principal axes are X6Y6Z6, which are defined by rotations Qx about the X4 axis and Qy about the Y5 axis. The center of mass offset of the rotor is g. Both the rotor and the platform are assumed to have unequal transverse inertias and the rotor is assumed to be dynamically and statically unbalanced. The equations of motion of this system are obtained by using Lagrangian formulation. Two cases are considered for unsymmetrical stiffness.

Microwave Spectrum of Ethyl Cyanide; r0-Structure, Nitrogen Quadrupole Coupling Constants and Rotation-Torsion-Vibration Interaction

An investigation of the microwave spectra of ethyl cyanide CH3CH2CN and the isotopes CH2DCH2CN, CH3CD2CN was carried out. The ground vibrational state of CH3CH2CN was reexamined under high resolution to give three centrifugal distortion constants DJ , DJK and DK. From the rotational constants of the ground vibrational state of CH3CH2CN, CH3CD2CN, CH2DCH2CN (symmetric) and CH2DCH2CN (asymmetric), CH3CH2 13CN and CD3CHDCN a r0-structure is derived. For the isotopes CH3CD2CN, CH2DCH2CN (symmetric) and CH2DCH2CN (asymmetric) the diagonal elements Χaa , Χbb and Χcc of the quadrupole tensor with respect to the principal axes of inertia were deduced from the hyperfine structure of the rotational lines. The off-diagonal element Χab for CH3CD2CN and CH2DCH2CN (symmetric) and the principal elements Χzz , Χxx of the quadrupole coupling tensor were obtained from Χaa, Χbb of the two molecules and from the principal axis rotation angle about the c-axis produced by isotopic substitution. For the analysis of the rotational spectra in the first excited states of methyl torsion and the lowest frequency in plane bending vibration of normal ethyl cyanide a molecular model with two internal degrees of freedom is considered. From the rotational line splittings in both states the coefficients V3 and V6 of the Fourier expansion of the potential hindering the internal rotation of the methyl group are determined.

Nuclear quadrupole coupling constants of cis-propylene imine from the microwave spectrum

The nuclear electric quadrupole hyperfine structure in the vibrational ground state of cis-propylene imine has been measured. The quadrupole coupling constants of the 14N nucleus with respect to the principal inertial axes of the molecule were found to be χaa = − 1.14 ± 0.06, χbb = + 2.01 ± 0.05, and χcc = − 0.88 ± 0.07 MHz.

Zur exakten Behandlung von kollektiven Rotational Teil B: Anwendungen / On the Exact Treatment of Collective Rotations. Part B: Applications

In part B we deal with some applications and conclusions of the theory for collective rotations of quantum mechanical systems which has been treated in part A. In the first section we investigate the consequences of a body-fixed coordinate-system lying in the principal axes of inertia. We find that for this choice in general no specific decoupling is obtained, and therefore the so-called hydrodynamic moments of inertia are always a lower limit for the real moments of inertia of a system. Further the transition from a n-body system to the rigid body is carried out. In another section the symmetry conditions of systems with identical particles are treated. Especially we study the question how to define the optimal body-fixed frame of reference in a system of independent identical particles. Finally we compare the results of our exact theory of collective rotations with the results of the cranking model and find that only in the limit of an infinitely heavy core the cranking model leads to an exact expression for the moment of inertia.

Spin stability of torque-free systems. I, II.

1) Figure 1 shows a system S consisting of a main body. B, and four antennas Ar (r = 1, ...,4). B is a rigid body having three (in general) unequal principal moments of inertia. Ar (r = 1,... ,4) are slender rigid bodies. That is, Ar possesses a central axis, Lr, such that the mass center, Ar*, of Ar lies on Lr; the moments of inertia of Ar about all lines passing through Ar* and normal to Lr are equal to each other; and the moment of inertia of Ar about Lr is negligible. Ar (r = 1,...,4) are attached to B at points Pr (r = 1,...,4) whose coordinates relative to X±, X2, X3, the principal axes of inertia of B for the mass center B* of B, are respectively (Rlt 0, #3), (Ri, R2> 0), (Rl9 0, -R3), (Rlt -R2, 0). The connection between Ar and B is effected by means of a revolute joint, a linear torsional spring, and a linear, viscous, torsional damper. The orientations of the axes of the joints, the spring constants, and the damping constants associated with these connections are given in Table 1, as are the distance from Pr to Ar*, the mass of Ar, and the moment of inertia of Ar about any line passing through Ar* and normal to Lr. Body B has a mass m and a moment of inertia Bt about Xt (i = 1, 2, 3). The system has four internal degrees of freedom. As we shall be concerned with motions during which the angles between Lr (r = 1,... ,4) and X1 remain constant, we use as generalized coordinates, qr (r = 1,... ,4), the radian measures of the deviations of the angles between Lr and X1 during a general motion from the constants values of interest, denoting the latter by a in the case of Al and A3, and by /I for A2 and A4, as indicated in Fig. 1. If the springs at Pr ( r=l , . . . ,4) are undeformed when ot + qr (r = 1,3) and P + qr (r = 2,4) are equal to zero, the system of forces transmitted by B to Ar is then equivalent to a force whose line of action passes through Pr, together with a couple whose torque, Tr (r = 1,... ,4), is given by Table 1 System parameters

On regular precessions of a heavy gyrostat: PMM vol. 37, n≗4, 1973, pp. 746–753

The regular precessions of a heavy asymmetric gyrostat are found by direct integration of the system of Zhukovskii equations written in the principal axes of inertia. The properties of these motions are investigated; the possibility of controlling them is revealed. Forces capable of causing a regular precession in the gyrostats are investigated. An idea was developed in [1] on the preferability of investigating the motion of a heavy gyrostat fixed at one point before the investigation of the motions of the classical rigid body ( ∗ ∗ Kharlamova E.I., Algebraic invariant relations of the differential equations of rigid body dynamics. Doctorate Dissertation, 1971. ) (see footnote on the next page). Still earlier [2] an attempt at such an investigation was made for an asymmetric gyrostat by Grioli's method and the dynamic possibility of regular precessions in such gyrostats was proved. Later on in [4] a solution of this problem was obtained in special nonprincipal axes of inertia, which was not written as a function of time.

The general equilibria of a spinning satellite in a circular orbit

Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body.