Helical Coupling Research Articles

Vibration Analysis Of A Motor-flexible Coupling-Rotor System Subject To Misalignment And Unbalance, Part II: Experimental Validation

Experimental studies were performed on a rotordynamic test apparatus to verify the theoretical model of shaft misalignment and rotor unbalance. A self-designed simplified flexible coupling and a commercial helical coupling were used in the experiments. The rotor shaft displacements were measured under the different misalignment and unbalance conditions. The measured and predicted frequency spectra were obtained. The theoretical predictions are in good agreement with the experimental measurements. Both the measured and predicted spectra show that unbalance and misalignment can be characterized primarily by one and two times shaft running speed, respectively. However, misalignment effects at times may not be apparent because the forcing frequency of misalignment (2 × shaft running speed) is not close enough to one of the system natural frequencies to excite the system appreciably. Therefore, in some cases the misalignment response is hidden and does not show up in the vibration spectrum. On the other hand, if 2 × shaft running speed is at or close to one of the system natural frequencies, the misalignment effect can be amplified and a high frequency density level at 2 × shaft running speed is pronounced in the frequency spectrum.

Exchange coupling in [Dy‖Er] metallic superlattices

Magnetic exchange coupling in metallic superlattices of [Dy‖Er], grown by molecular-beam epitaxy, has been examined by neutron diffraction. In a superlattice of 65-Å layers of Dy and 55-Å layers of Er, distinct ordering temperatures were observed for the Dy and Er layers. Basal plane helical ordering of the Dy layers was initiated at temperatures close to TN for bulk Dy (178 K) with a long-range interaction, preserving both phase and chirality, mediated through the Er layers. At a temperature near 70 K, the helical coupling of the Dy spins is replaced by an antiferromagnetic coupling of adjacent ferromagnetically ordered Dy layers coexisting with a remanent helical order. At a temperature well below TN of bulk Er, c-axis ordering of the Er spins occurs in the superlattice, and in measurements at 10 K there is evidence of basal plane moment ordering in the Er.

Electromagnetic interactions of hadrons in the relativistic harmonic-oscillator quark model

Various electromagnetic properties of hadrons are investigated systematically by applying many possible types of ''minimal currents'' in the framework of the relativistic harmonic oscillator (H.O.) which are conserved in the symmetric limit. As a result it is shown that a general minimal current in the SU(6)/sub M/ scheme (minimally boosted SU(6)) with definite-metric H.O. reproduces satisfactorily experimental behaviors of almost all hadron electromagnetic (EM) properties: EM form factors of nucleons and pions (including nonvanishing electric form factor of the neutron), magnetic and transition moments of ground-state mesons and baryons, and helicity couplings of photon and baryon resonances. Other types of currents, a vector-meson-dominant one and a general minimal one in the U (12) scheme with shell-type definite-metric H.O., are also interesting in giving similar desirable behaviors with some exceptions.

Partial-wave analysis of the dilatation-invariant relativistic S-matrix I Clebsch-Gordan coefficients for the Weyl group

As a first step towards partial wave analysis of a dilatation invariant S-operator, the Clebsch-Gordan coefficients for the Weyl group W (i.e. Poincaré group extended by dilatations) are derived using Mackey's theory of induced representations. Three cases of helicity coupling of two physical irreducible representations of W with any spin are treated: (a) m 2 1>0, m 2 2>0, (b) m 2 1>0, m 2 2=0, (c) m 2 1=0, m 2 2=0.

Decomposition of the Tensor Product of two Imaginary Mass Representations of the Poincaré Group

The reduction of the tensor product is carried out by a method that is completely analogous to that used for real mass representations in the helicity coupling. This is possible through the use of a continuous basis for the UIRs of the little group SU(1,1). The Clebsch-Gordan coefficients are obtained in the same simple form as in the real mass case.

Covariant arbitrary-spin wave functions and helicity couplings

Arbitrary-spin wave functions are developed in a realization-independent manner for all polarization states and then given explicitly in a covariant notation. Vertex functions are parametrized in a way which leads automatically to the use of helicity couplings. Conversion tables relating covariant parity-conserving helicity couplings to more conventional tensor and spinor-tensor couplings are given.

Threshold conditions for helicity amplitudes

By relating the helicity coupling scheme to thel-s and multipolar schemes we derive relations between helicity amplitudes at threshold both for massive particles and for photons; for photons the relations have to be supplemented by a low-energy theorem on invariant amplitudes. In the case of πN scattering we show how the threshold conditions can be used to obtain kinematic-singularity-free amplitudes with improved asymptotic behaviour.

Unified Unitary Representation of the Poincaré Group for Particles of Zero and Positive Rest Mass

As is well known, Wigner's construction of the unitary representations in terms of little groups gives quite dissimilar forms for the cases m = 0 and m > 0, while the spinor representation which does give a unified description of the above two cases is not unitary. We point out that it is quite possible to give a unified unitary representation for both cases (Sec. 1). This is achieved simply by noting that, while the factorization of U(Λ) corresponding the choice of the little group of (1, 0) is not valid for m = 0, the explicit final expression for the Wigner rotation Rw and the corresponding infinitesimal generators remain perfectly well defined for m = 0, and continue to furnish a unitary (discrete spin) representation for this case, which is compatible with the restriction of helicity to a particular fixed value. Moreover, the representation thus obtained has a very simple and direct geometrical significance. The relation of our formulation with that of Wigner is studied (in Sec. 2) and the comparison with the spinor representations is given (Sec. 3). We rederive our representation, starting from a particular simple condition (4.1) (in Sec. 4) which holds for both cases (m = 0, m > 0). We then consider (Sec. 5) the application of our unified formulation to the reduction of direct products, involving particles of positive and zero rest mass, comparing the result with that of helicity coupling. In the Appendix we make certain remarks concerning the Hermiticity of the generators and the possibility of defining a position operator for m = 0. Comparison with Foldy's representation is given (in the Appendix and Sec. 3), explaining why his representation cannot be considered to be strictly unitary, though the relation with the unitary case is quite a simple one.

On the Unitary Representations of the Galilei Group. II. Two-Particle Systems

Mackey's theory is used to study the kinematics of a nonrelativistic two-particle system. We consider the helicity coupling and the l-S coupling and derive a Jacob-Wick's formula relating these two couplings (Glebsch-Gordan coefficients).