Variable Moment Of Inertia Research Articles

Rotational spectra of nuclei: equivalence of a superfluid liquid model, the cranking model and a model with a variable moment of inertia

It is shown that a model of a superfluid Fermi liquid with triplet Cooper pairing in the case of strong spin-orbit coupling gives rise, for some superfluid phases, to the same rotational spectra of nuclei as the cranking model and/or a model of a variable moment of inertia. An ability of these models to describe superdeformed bands in the A approximately 190 region is demonstrated.

Model of superfluid liquid with triplet pairing, cranking model and model of variable moment of inertia in superdeformed bands inA?190 region

The triplet pairing model, which has been shown, in some cases, to be equivalent to the cranking and/or variable moment of inertia models, is used to describe the superdeformed bands inA∼190 region. The two-parameter expression for theγ-transition energiesEγ(I), common to these three models, allows a good description of experimental data and an unambiguous spin assignment for the states of these superdeformed bands.

A mathematical model of body kinematics in swimming tadpoles

A mathematical model is described that predicts the body kinematics of tadpoles swimming in a straight line at constant velocity. The model is a forced beam with a variable moment of inertia and cross-sectional area. The beam is free at both ends and forced cyclically at the position that corresponds to the base of the tail in a real animal. This forcing regime simulates the real contraction of locomotor muscles. Finite-dimensional numerical techniques were used to approximate the solution. The lowest predicted fundamental frequency of vibration should be the resonant frequency of vibration of the tadpole. The predicted resonant frequency and the observed swimming frequencies were in good agreement.

Is there objective evidence for quantized spin alignment in superdeformed nuclei?

It is impossible to determine spins for superdeformed bands by fitting the \ensuremath{\gamma}-transition energies alone. It is necessary to introduce a model. By using a variable moment of inertia (VMI) model one can estimate spins but cannot rule out the possibility of a \ifmmode\pm\else\textpm\fi{}\ensuremath{\Elzxh} uncertainty. Therefore, no objective evidence exists requiring the presence of quantized spin alignment in superdeformed nuclei. An alternative hypothesis that all superdeformed nuclei in a given mass region have the same VMI core, and thus essentially no alignment until high-N Coriolis effects become significant, seems to explain the present data.

B(E2) transition probabilities in the q-rotator model with SUq(2) symmetry

The SUq(2) symmetry of the q-rotator model, which for rotational bands predicts squeezing of the energy levels equivalent to the variable moment of inertia (VMI) model, predicts an increase with angular momentum of the B(E2) transition probabilities among these levels, while the rigid rotor model predicts saturation and the interacting boson model predicts a decrease. Some evidence supporting the SUq(2) prediction is presented. The possible usefulness of the quantum algebraic method in extending the VMI concept to B(E2) transition probabilities is pointed out.

Nuclear alignment: Classical dynamical model for the 238U-238U system.

Dynamical properties of the $^{238}\mathrm{\ensuremath{-}}^{238}$U system at the classical turning point, specifically the distance of closest approach, the relative orientations of the nuclei, and deformations have been studied at the sub-Coulomb energy of ${\mathit{E}}_{\mathrm{lab}}$=6.07 MeV/nucleon using a classical dynamical model with a variable moment of inertia. Probability of favorable alignment for anomalous positron-electron pair emission through vacuum decay is calculated. The calculated small favorable alignment probability value of 0.116 is found to be enhanced by about 16% in comparison with the results of a similar study using a fixed moment of inertia as well as the results from a semiquantal calculation reported earlier.

Influence of the moment of inertia of the pendulum on the internal friction (loss tangent) measured by free decay

The internal friction (loss tangent) of solids is normally measured, as a function of temperature, with a torsion pendulum operating in free decay. Curves of the internal friction and the oscillation frequency, against temperature, are obtained at various moments of inertia, to extract the parameters characteristic of the relaxation process (relaxation time and strength). In all these experiments only the temperature is considered as an independent variable and the moment of inertia of the pendulum is mainly used to shift the internal friction peaks in the temperature scale. It is pointed out in the paper that the moment of inertia is also an independent variable which can be used to determine, with high accuracy, if the measured peak is of the Debye type or not. A new torsion pendulum, with continuously variable moment of inertia is presented, which allows measurements of the partial derivative of the internal friction and the oscillation frequency with respect to the moment of inertia, at constant temperature. Finally, some measurements of the Snoek relaxation in Nb-O alloys are presented, to show the applicability of the concepts developed in the paper.

Fixed‐End Moments and Thrusts of Planar Curved Beams

Formulas of fixed-end moments and thrusts for a curved member of constant section subjected to a uniformly distributed in-plane load are presented. Expressions are derived for noncircular curved beams of cycloidal, catenary elliptic, and sine shapes. For curved beams of circular and parabolic shapes, expressions can be found from the works of Parcel and Moorman, and Leontovich. Given a curved beam with the known beam-height-to-span ratio and loading, the fixed-end moments and thrusts can be obtained from the derived expressions. Finally, with some modifications, the present investigation can be applied to curved beams of variable moment of inertia.

Robotics: designing the mechanisms for automated machinery

Preface to the Second Edition. Introduction: Brief Historical Review and Main Definitions: What Robots Are. Definition of Levels or Kinds of Robots. Manipulators. Structure of Automatic Industrial Systems. Nonindustrial Representatives of the Robot Family. Relationship between the Level of Robot 'Intelligence' and the Product. References. Concepts and Layouts: Processing Layout. How Does One Find the Concept of an Automatic Manufacturing Process?. How to Determine the Productivity of a Manufacturing Process. The Kinematic Layout. Rapid Prototyping. Dynamic Analysis of Drives: Mechanically Driven Bodies. Electromagnetic Drive. Electric Drives. Hydraulic Drive. Pneumodrive. Brakes. Drive with a Variable Moment of Inertia. Kinematics and Control of Automatic Machines: Position Function. Camshafts. Master Controller, Amplifiers. Dynamic Accuracy. Damping of Harmful Vibrations. Automatic Vibration Damping. Electrically Controlled Vibration Dampers. Feedback Sensors: Linear and Angular Displacement Sensors. Speed and Flow-Rate Sensors. Force Sensors. Temperature Sensors. Item Presence Sensors. Transporting Devices: General Considerations. Linear Transportation. Rotational Transportation. Vibrational Transportation. Feeding and Orientation Devices: Introduction. Feeding of Liquid and Granular Materials. Feeding of Strips, Rods, Wires, Ribbons, Etc. Feeding of Oriented Parts from Magazines. Feeding of Parts from Bins. General Discussion of Orientation of Parts. Passive Orientation. Active Orientation. Logical Orientation. Orientation by Nonmechanical Means. Functional Systems and Mechanisms: General Concepts. Automatic Assembling. Special Means of Assembly. Inspection Systems. Miscellaneous Mechanisms. Manipulators: Introduction. Dynamics of Manipulators. Kinematics of Manipulators. Grippers. Guides. Mobile and Walking Robots. Solutions to the Exercises. Recommended Readings. List of Main Symbols. Index.

Reformulation of the variable moment of inertia model in terms of nuclear softness.

The ground-state bands in even-even nuclei are studied by treating the variation of moment of inertia with angular momentum in terms of the relative increase of moment of inertia with angular momentum, called the softness parameter. Such a reformulation of the variable moment of inertia (VMI) model in terms of the various orders of softness of the nuclear softness (NS) model extends the range of validity of the new model, called VMINS, to 2.0\ensuremath{\le}${\mathit{R}}_{42}$\ensuremath{\le}3.33. This gradual softening of the rigid rotator throughout the Periodic Table requires softness parameter to, at least, second order, with the vibrational energy also becoming important for very soft nuclei.

Free vibrations of continuous beams with singularities in inertia and stiffness distribution

The free vibrations of continuous beams with singularities in inertia and stiffness distribution are presented in this paper. Simple closed-form mathematical expressions for the mode shapes of vibrations are obtained using Galerkin's approach. Several numerical examples of structures with known exact solutions are presented to show the accuracy of the method. Also, examples of a simple beam with intermediate elastic translational and rotational supports carrying point and rotational mass, a two-span continuous beam with variable moment of inertia and mass distribution and a single-span beam with fixed end and overhanging cantilever are presented to show the applicability of the method

Equivalent systems for inelastic analysis of non-prismatic members

The research in this paper involves the analysis of non-prismatic members where the material is permitted to be stressed well beyond its elastic limit, thus causing the modulus of elasticity to vary along the length. The deflection characteristics of such members are determined by using the first author's method of the equivalent systems (see for example Fertis [D. G. Fertis, Dynamics and Vibration of Structures. John Wiley, New York (1973); D. G. Fertis, Dynamics and Vibration of Structures (revised edition). Robert E. Krieger, Malabar, FL (1984)], Fertis and Keene [D. G. Fertis and M. E. Keene, J. struct. Engng, Proc. ASCE 16 (1990)] and Fertis and Pallaki [D. G. Fertis and S. Pallaki, J. Engng Mech., Proc. ASCE 115 (1989)]), which permits replacement of the original member of variable stiffness E x I x with one of uniform stiffness E 1 I 1, whose elastic line is identical to the one of the original variable stiffness member. It is proven mathematically that the inelastic analysis of members with variable moment of inertia I x and variable modulus of elasticity E x can be carried out by using equivalent linear systems of constant stiffness E 1 I 1 and applying known methods of linear elementary mechanics. The member can be analyzed for both elastic and inelastic ranges, all the way to failure, thus permitting observation of progressive deterioration of the member's ability to resist stress and deformation, and establish useful practical critical limits regarding these properties.

Concept of a modified flywheel for megajoule storage and pulse conditioning

The concept of a flywheel with a variable moment of inertia for electromagnetic launch (EML) is introduced. The modified flywheel will further improve the energy density and efficiency. Coupled to a pulse-duty generator, it could produce a near-square pulse or other desirable pulse shapes. The amount of energy, its rate, and its switching all could be controlled prior to electric energy conversion. The modified flywheel is structured with masses movable along radial paths. Potential energy is stored with respect to mass position and kinematic energy with respect to spin. This mass positioning provides a means to control the rate of energy discharge. Control with spring-loaded weight would have near constant spin output. A servomechanism scheme can, however, provide the precise inward-moving positioning control of masses, and hence the other desirable output pulse conditioning. In the conventional flywheel, energy is always discharged in an exponential decay. In an EML system, a flywheel is the rotor of the pulse-duty generator, such as in the homopolar generator, compulsator, or the disk alternator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SU q(2) description of rotational spectra and its relation to the variable moment of the inertia model

Rotational spectra of even-even nuclei can be described by the quantum algebra SU q (2). The two-parameter formula given by the algebra is equivalent to an expansion in terms of powers of j( j + 1), similar to the expansion given by the variable moment of inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values.

Application of Adaptive Control on a Simple Arm

This work describes yet another application of adaptive control, this time to an arm with two-degrees-of-freedom and variable moment of inertia. The control aim is to accomplish a desired transfer function in the system while minimizing the moment of inertia effects (constant damping ratio). The system to be controlled is described by a simple linear discrete model with a minimum of parameters to be estimated. A number of approaches in adaptive control have been integrated to a controller suitable for our purposes. The result was a direct adaptive control, in which the gain and the coefficient of the moment of inertia were estimated. Similar controller was applied to both axes. Applying the controller resulted in an appropriate tracking with desired damping and minimum sensitivity to change of arm load.

Inelastic analysis of variable stiffness members

The research in this paper involves the analysis of non-prismatic members where the material is permitted to be stressed well beyond its elastic limit, thus causing the modulus of elasticity to vary along their length. The deflection characteristics of such members are determined by using the first authors method of the equivalent systems, see for example Fertis (1973, 1984), Fertis and Keene (1990), and Fertis and Pallaki (1989), which permits to replace the original member of variable stiffness E xI x with one of uniform stiffness E 1I 1, whose elastic line is identical to the one of the original variable stiffness member. It is proven mathematically that the inelastic analysis of members with variable moment of inertia I x and variable modulus of elasticity E x can be carried out by using equivalent linear systems of constant stiffness E 1I 1 and applying known methods of linear elementary mechanics. The member can be analyzed for both elastic and inelastic ranges, all the way to failure, thus permitting to observe progressive deterioration of the member's ability to resist stress and deformation, and establish useful practical critical limits regarding these properties.

Use of Positional Parameter in Rayleigh's Method

The determination of the response of a beam of variable moment of inertia when subjected to an eccentric compressive load is addressed. The beam displacement is approximated in terms of a simple polynomial coordinate function which contains two parameters which allow for two separate minimizations of the governing functional. One of the parameters appears as an exponent of the coordinate function while the other depends upon the origin of the coordinate system. It is shown that the proposed approach yields excellent accuracy in the case of a beam of uniform cross section.

Identification of Time Varying Parameters of the Robot Dynamics

The robot dynamics consists of the dynamics of the mechanics, the servo-drives, and the robot controller structure. The dynamics of the mechanics is simulated by the equation of motion which is set up automatically by a computer program. The robot controller is taken into account too, to simulate the robot dynamics. In order to control the robot axes decoupled, the moment at support, nonlinear effects as the Coulomb friction and the variable moment of inertia has to be known. Therefore an extended Kaiman filter is designed and tested, to identify these signals. Since the filter is based upon a linearization it is very sensitive to the start a-priori estimate and co-variances and the driving motor torque.

Variable moment of inertia in the interacting boson model.

We present a simple prescription for the determination of the nuclear softness parameter, a measure of low-spin variation of the moment of inertia, in the interacting boson model. The formulation makes use of explicit dependence of the moment of inertia on the d-boson mixing parameter. The systematics of the softness parameter are carried out using an effective interacting boson model Hamiltonian approach and results are found to be in excellent agreement.

Stiffness Coefficients of Noncircular Curved Beams

The stiffness coefficient matrix for a curved member of constant cross section considering the effect of flexural deformation is presented. This matrix relates the member-end rotations, vertical deflections, and horizontal translations to the internal bending moments, vertical shears, and horizontal thrusts. Expressions of the stiffness coefficients have been derived for noncircular curved beams of cycloidal, catenary, elliptic, and sine shapes. For curved beams of circular and parabolic shapes, expressions can be found from the writers' previous work. For a given curbed beam with the beam-height-to-span ratio known, the stiffness coefficients can be obtained from the derived expressions. Finally, with some modifications, this matrix can be applied to curved beams of variable moment of inertia.