A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

Rotating crystal ESR cavity for angular variation studies at room temperature

We describe an X-band ESR cavity for angular variation studies on single crystals at room temperature. The cavity was found to have a high Q over wide rotation angles. Review of Scientific Instruments is copyrighted by The American Institute of Physics.

Analysis of Raman bandwidths and bandshapes of glasses through their glass-transition temperatures

Raman bandwidths and bandshapes of some molecular and ionic glasses have been investigated through the glass-transition region. Widths of both polarised and depolarised bands exhibit step-like changes during the glass transition. Molecular and ionic glasses differ with respect to the magnitude and the nature of variations in bandwidths and reorientational times. An attempt has been made to understand the changes in bandwidths around the glass-transition temperature.

Polarized Ethylenes: Structure of 2-Benzoyl-3-dimethylamino-3-methylthlo-2-propenenitrile

C13H14N2OS, M r = 246, is monoclinic, P21/c, with a = 7.214(1), b = 8.935(5), c = 20.243 (6) A, fl =99.42 (2) °, V = 1304.83 ,~3, Z = 4, D m = 1.23, D x =1.25 Mg m -3, p(Mo Ka, 2 = 0.7107 A) = 0.232 mm -~,F(000) = 520. The structure was solved by direct methods and refined to an R value of 0.042 using 1127 intensity measurements. The C=C and C-N bond distances differ considerably from their normal values. An appreciable rotation [38.3(4) °] about the C=C bond is observed, the bond length being 1.414(5)A.This is due to the combination of push-pull and steric effects.

Unsteady Free-Convection Flow on a Rotating flat-Plate Under Nonuniform Gravity

The free convection problem with nonuniform gravity finds applications in several fields. For example, centrifugal gravity fieldsarisein many rotating machinery applications. A gravity field is also created artificially in an orbital space station by rotation. The effect of nonuniform gravity due to the rotation of isothermal or nonisothermal plates has been studied by several authors [l-5] using various mathematical techniques.

Has the Crab Pulsar Magnetic-Field Grown After its Birth

We investigate the evolution of rotation period and spindown age of a pulsar whose surface magnetic field undergoes a phase of growth. Application of these results to the Crab pulsar strongly indicates that its parameters cannot be accounted for by the field growth theories.

NMR (1H, 13C) and MO (ab initio, CNDO/2, EHT) studies on basic and N-protonated hydrazinecarbothioamide

The conformational preferences of hydrazinecarbothioamide (HCTA, H2NNHCSNH2) in its basic and N-protonated (PHCTA, H3NNNHCSNH2) forms have been studied by 1H and 13C NMR spectroscopy and by theoretical LCAO-MO methods (ab initio, CNDO/2 and EHT). The hindered rotation around the C---N bond has been investigated by a total line shape analysis for the thioamide protons and by the three MO methods. Changes in the molecular conformation and electronic structure on protonation are briefly discussed.

A comparison of the molecular orbital (ab initio, CNDO and EHT) methods applied to the conformational study of thiocarbonohydrazide in its basic and diprotonated forms

Conformational preferences of thiocarbonohydrazide (H2NNHCSNHNH2) in its basic and N,N′-diprotonated forms are examined by calculating the barrier to internal rotation around the C---N bonds, using the theoretical LCAO—MO (ab initio and semiempirical CNDO and EHT) methods. The calculated and experimental results are compared with each other and also with values for N,N′-dimethylthiourea which is isoelectronic with thiocarbonohydrazide. The suitability of these methods for studying rotational isomerism seems suspect when lone pair interactions are present.

Zeeman effect of chlorine nuclear quadrupole resonance and hydrogen bonding in 2,6-, 2,5- and 3,5-dichlorophenols

The Zeeman effect of chlorine nuclear quadrupole resonance in polycrystalline samples of 2,6-, 2,5 and 3,5-dichlorophenol has been investigated at room temperature in order to study the effect of hydrogen bonding on the electric field gradient asymmetry parameter n. While the two n.q.r. lines in 3,5-dichlorophenol gave an asymmetry parameter of 10%, those in 2,6- and 2,5-dichlorophenol gave different values of n for the two chlorines. The chlorine atom which is ortho to the OH group and involved in hydrogen bonding (i.e., corresponding to the low frequency line) gave an asymmetry parameter of 0.21 in 2,6-dichlorophenol and 0.17 in 2,5-dichlorophenol while the other chlorine (i.e., corresponding to the high frequency line) gave a lower value of 0.12 in 2,6-dichlorophenol and 0.11 in 2,5-dichlorophenol. These values of n are discussed in terms of hydrogen bonding and bond parameters.

A technique for steady-state polarisation of stationary solid electrodes and its applications

A new technique has been devised to achieve a steady-state polarisation of a stationary electrode with a helical shaft rotating coaxial to it. A simplified theory for the convective hydrodynamics prevalent under these conditions has been formulated. Experimental data are presented to verify the steady-state character of the current-potential curves and the predicted dependence of the limiting current on the rotation speed of the rotor, the bulk concentration of the depolariser and the viscosity of the solution. Promising features of the multiple-segment electrodes concentric to a central disc electrode are pointed out.

Non-linear flapping vibrations of rotating blades

The non-linear equations of motion of a rotating blade undergoing extensional and flapwise bending vibration are derived, including non-linearities up to O (ε3). The strain-displacement relationship derived is compared with expressions derived by earlier investigators and the errors and the approximations made in some of those are brought out. The equations of motion are solved under the inextensionality condition to obtain the influence of the amplitude on the fundamental flapwise natural frequency of the rotating blade. It is found that large finite amplitudes have a softening effect on the flapwise frequency and that this influence becomes stronger at higher speeds of rotation.

Molecular conformation of N,N -diarylthioureas: An assessment by 1H NMR and infrared spectroscopy

Several N,N -dipyridyl- and N-phenyl-N -pyridyl-thioureas were examined in different solvents at various temperatures by 1H NMR in order to study their conformational properties. The influence of concentration and the methyl substituent in the pyridine ring on the chemical shifts of the NH and pyridine groups was investigated. The observed chemical shifts are analysed in terms of the conformational properties of the molecules. Free energy barriers to the internal rotation about the C N bonds have been determined. Infrared spectra have been measured to supplement the NMR studies. Intramolecular hydrogen bonding played a major role in the preferred conformation of pyridylthioureas. The data further revealed an interesting dynamic exchange phenomenon occurring in symmetric N,N -dipyridylthioureas between two intramolecularly hydrogen bonded conformers.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Heat transfer in a MHD flow between eccentric disks rotating at different speeds

Heat transfer in a MHD flow between two infinite eccentric disks rotating with different speeds is considered when the plates are maintained at different temperatures. The results for the corresponding nonmagnetic case presented wrongly by Banerjee and Borkakati [7] are corrected. It is observed that the eccentric rotation reduces the heat transfer on the disks.

X-ray and ultraviolet photoelectron spectroscopy studies of the interaction of carbon monoxide with oxygen adsorbed on silver covered with potassium, caesium or barium

X-ray and He(II) ultraviolet photoelectron spectroscopy studies of the interaction of CO with oxygen on potassium-, caesium- and barium-covered Ag surfaces have shown the formation of carbonate at 300 K. While on a caesium-covered surface only carbonate formation takes place, on the potassium- and barium-covered surfaces molecularly chemisorbed CO is also formed. The variation of the surface concentrations of carbon and oxygen with temperature has been examined and a reaction sequence for the interaction of CO with adsorbed oxygen on potassium-, caesium- and barium-covered Ag surfaces is suggested.