Showing papers on "Degrees of freedom published in 1987"

Some Common Problems in Log-Linear Analysis:

Abstract: Several problems often encountered in research using log-linear models for categorical response variables are discussed. The issues covered are (a) determining the degrees of freedom for a model, (b) analyzing sparse data, (c) analyzing weighted data, (d) modeling rates, and (e) interpreting results.

Finding collision-free smooth trajectories for a non-holonomic mobile robot

Abstract: Most mobile robots are subject to kinematic constraints (non-holonomic Joints), i.e., the number of degrees of freedom is less than the number of configuration parameters. Such navigate in very constrained space, but at the expense of backing up maneuvers [Laumond 86]. In this paper we study the original problem of finding collision-free smooth trajectories, i.e. with never backing up, for a circular mobile robot whose the turning radius is lower bounded.

Common Structure of Techniques for Choosing Smoothing Parameters in Regression Problems

Abstract: On tente de relier deux methodes de choix du parametre de lissage, l'une basee sur la mesure du risque et l'autre sur le degre d'ajustement de la regression aux donnees

Stability Theory: An Introduction to the Stability of Dynamic Systems and Rigid Bodies

Abstract: This book describes a unified theory of stability for systems of rigid bodies with finite degrees of freedom and for continuous elastic bodies with infinite degrees of freedom. This involves extending the direct method of Lyapunov so that it can be used to evaluate the stability of continuous elastic bodies. Special attention has also been paid to a dynamical treatment of the stability of these bodies, and the existence of nonconservative follower forces has been taken into account. For this second edition the author has fully revised and updated his material; in particular, the section on elastomechanics has been completely rewritten to include the major developments which have taken place in this area. Exercises for the reader have been added at the end of each chapter.

The Energy Method

Abstract: For conservative scleronomic systems with finite degrees of freedom it is common to apply the so-called energy method for the assessment of the stability of a particular motion of the system. Very frequently, the particular ‘motion’ is a stationary (equilibrium) position of the system. Then, the theorem of Dirichlet1 holds which states that the equilibrium is stable if the potential energy of the system assumes a minimum in the equilibrium position.

On the Nuclearity Condition for Massless Fields

Abstract: It is shown that quantum field theories of free massless particles satisfy a recently proposed ‘nuclearity condition’ restricting the admissible number of local degrees of freedom of a theory. This result is based on an improved bound for the ‘nuclearity index’ of certain specific sets of vectors in Fock space.

Selection of Degrees of Freedom for Dynamic Analysis

Abstract: A technique for the selection of dynamic degrees of freedom of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for component mode synthesis is presented. Generally, the selection of DDOF is left to the judgement of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenvalue problem of components mode synthesis. The execution of this technique is discussed in this paper. Examples of using this technique in conjunction with a general purpose finite element computer program are given.

Vibrations and transient responses of Timoshenko beams resting on elastic foundations

Abstract: A finite element technique is used to obtain the natural frequencies and transient responses of Timoshenko beams resting on elastic foundations The beam is discretized into beam elements, each with four degrees of freedom The equations of motion in terms of the nodal degrees of freedom are derived by applying Hamilton's principle The numerical results for a hinged-hinged beam are given to show the effects of rotatory inertia, shear deformation and foundation constants on the natural frequencies of the beam The transient responses of beams are subsequently presented and compared with the available solutions

Activated barrier crossing for many degrees of freedom: Corrections to the low friction Kramers result

Abstract: We evaluate corrections to the activated barrier crossing rate constant for the Kramers model at low friction γ for n strongly coupled degrees of freedom. The rate constant behaves as γ(1−const γ1/(n+1)+⋅⋅⋅) at low γ. As n increases the correction terms become increasingly important and they will substantially diminish the rate constant in a physically accessible low friction regime.

Dynamic stiffness and response analysis

Abstract: The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method has been extended to frame structures with uniform or non-uniform, straight or curved, damped or undamped beam members. An orthonormal condition is suggested here for the natural modes resulting from the dynamic stiffness method; modal analysis in the classical sense is then made possible. Modes corresponding to repeated natural frequencies are discussed in detail. An expansion theorem for expanding from a finite number of degrees of freedom by means of an infinite number of modes is validated by means of the frequency-dependent shape functions. Distributed modal participation factors are introduced for distributed excitations.

Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Point Trajectories

Abstract: A general framework is presented for the study of the properties of trajectories generated by points embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Quantities are developed to characterize point trajectories generated by different mechanisms and to distinguish between different positions along the same trajectory. Point trajectories are classified into three types according to whether the number of degrees of freedom is less than, equal to, or greater than the dimension of the space in which the motion takes place. Local and global motion properties are developed for each of these three cases. A new way of using the redundant degrees of freedom in (redundant) mechanisms is presented. These analysis techniques are applied to two- and three-degrees-of-freedom mechanisms containing rotary and prismatic joints.

Non-oriented spin-1 systems

Abstract: A maximal state of spin polarisation of a spin-1 system with all eight degrees of freedom (namely, three distinct axes and two non-zero scalars) is realised when a spin-1 nucleus with nonzero electric quadrupole moment is embedded in a suitable crystal lattice generating an electric quadrupole field and is exposed to an external constant magnetic field whose direction does not coincide with any of the principal axes characterising the electric quadrupole field. In the absence of the magnetic field only five of the eight degrees of freedom (i.e. two distinct axes and a nonzero scalar) are realised if the asymmetry parameter eta not=0. If eta =0 the two axes coalesce. This suggestion is made to stimulate experimental efforts to produce polarised multiaxial spin-1 targets.

Coherent structures and dynamical systems

Abstract: Any flow of a viscous fluid has a finite number of degrees of freedom, and can therefore be seen as a dynamical system. A coherent structure can be thought of as a lower dimensional manifold in whose neighborhood the dynamical system spends a substantial fraction of its time. If such a manifold exists, and if its dimensionality is substantially lower that that of the full flow, it is conceivable that the flow could be described in terms of the reduced set of degrees of freedom, and that such a description would be simpler than one in which the existence of structure was not recognized. Several examples are briefly summarized.

Bias of Effective Degrees of Freedom of a Spectrum

Abstract: Estimates of the effective number of degrees of freedom for integrals of a spectrum (e.g., significant wave height) are shown to be biased. The mean value of estimates of the effective degrees of freedom from unsmoothed spectra is one-half of the true value for a smoothed spectrum. Numerical simulations of JONSWAP spectra and field data agree well with the theoretical results.

Temporal and spatial structures of nonlinear dynamical systems

Abstract: The present article contains the description of simple experiments mounted for a demonstration of temporal and spatial structures of dissipative nonlinear dynamical systems. The systematic approach possible to systems with few degrees of freedom is described on an elementary level showing experiments on a rotating nonlinear oscillator. The temporal structure elements are those contained in the stationary, periodic, quasi-periodic, and chaotic motion. Structures of systems with many degrees of freedom are demonstrated by showing experiments on real spatially extended electronic circuits and gas discharge systems both described by reaction diffusion equations. Such systems have a complexity and richness of structures far beyond what can be described systematically by current techniques. However, for special cases a quantitative understanding is possible. Also filaments of rather well defined size and shape observed in our experiments can be considered as simple elements building up a variety of spatial patterns. We also show that noise is decisive in many cases for the formation and the nonreproducibility of stationary structures. Finally, we stress some features common to reaction diffusion systems and living beings.

An alternative method for minimization of the driving forces in redundant manipulators

Abstract: A discretized equation allows the acceleration terms to be changed to velocity terms in the definition of joint driving forces in robotic manipulators. An eleven degrees of freedom, three dimensional robotic manipulator is used in a numerical example to test the developed algorithm. Numerical and algorithmic stabilities are also discussed.

Toy construction apparatus

Abstract: An assembly toy comprising a plurality of engaged interconnectable elements, each interconnectable element including a generally planar surface and comprising at least one engagement portion selected from first and second types of mutually interconnectable engagement portions, individual ones of the first and second types of mutually interconnectable engagement portions, when engaged permitting relative displacement of the elements interconnected thereby with a plurality of degrees of freedom.

A Floating-Lens Actuator

Abstract: An actuator for optical recorder applications is described in which the objective lens is electromagnetically suspended in a configuration of magnetic coils, free from mechanical contact. The coil configuration is such that the lens can be driven in five degrees of freedom. An optical strategy has been devised to generate the necessary error signals for servo control.