Stability of Dynamic Systems

1983 ◽  
Vol 50 (4b) ◽  
pp. 1086-1096 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Degrees Of Freedom ◽  
Continuous Systems ◽  
Specific Nature ◽  
Stability Problems ◽  
Comprehensive Theory ◽  
Elastic Systems

It is shown how stability theory of dynamic systems, emerging from various beginnings strewn over the realm of mechanics, developed into a unified, comprehensive theory for dynamic systems with a finite number of degrees of freedom. It is then demonstrated, how such theory could be adapted over the last five decades to the specific nature of stability problems involving continuous elastic systems. The need for such adaption is stressed by pointing to systems with follower forces. The difficulties arising from the fact that continuous systems are systems with an infinite number of degrees of freedom are emphasized, and an adequate approach to a unified stability theory including also continuous systems is outlined.

scholarly journals AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF FREEDOM OF MASSES BY SUPERIMPOSING ADDITIONAL CONSTRAINTS

2021 ◽  
Vol 17 (2) ◽  
pp. 76-82
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov
Keyword(s):  
Finite Number ◽  
Frequency Spectrum ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic Plates ◽  
Natural Vibrations ◽  
Design Constraint ◽  
Elastic Systems ◽  
The Masses ◽  
Additional Constraints

As is known, for some elastic systems with a finite number of degrees of freedom of masses, for which thedirections of motion of the masses are parallel and lie in the same plane, methods have been developed for creatingadditional constraints that purposefully change the spectrum of natural frequencies. In particular, theory and algorithm forthe formation of aimed additional constraints have been developed for the rods, the introduction of each of which doesnot change any of the modes of natural vibrations, but only increases the value of only one frequency, without changingthe values of the remaining frequencies. The distinctive paper is devoted to the method of forming a matrix of additionalstiffness coefficients corresponding to such aimed constraint in the problem of natural vibrations of rods. This method canalso be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which thedirections of motion of the masses are parallel, but not lie in the same plane. In particular, such systems include plates.However, the algorithms for the formation of aimed additional constraints, developed for rods and based on the propertiesof rope polygons, cannot be used without significant changes in a similar problem for plates. The method for the formationof design constraint schemes that purposefully change the spectrum of frequencies of natural vibrations of elastic plateswith a finite number of degrees of freedom of masses, will be considered in the next work.

Mesoscopic Continuous and Discrete Channels for Quantum Information Transfer

2006 ◽  
Vol 13 (03) ◽  
pp. 273-280
Author(s):  
Ferdinando de Pasquale ◽  
Gian Luca Giorgi ◽  
Simone Paganelli
Keyword(s):  
Quantum Information ◽  
Finite Number ◽  
Infinite Number ◽  
Anderson Model ◽  
Weak Coupling ◽  
Information Transfer ◽  
Degrees Of Freedom ◽  
Quantum State Transfer ◽  
State Transfer ◽  
Discrete Channels

We study the possibility of realizing perfect quantum state transfer in mesoscopic devices. We discuss the case of the Fano-Anderson model extended to two impurities in a single excitation regime. For a channel with an infinite number of degrees of freedom, we obtain coherent behaviour in the case of strong coupling or in weak coupling off-resonance. For a finite number of degrees of freedom, coherent behaviour is associated to weak coupling and resonance conditions.

Hamiltonian formulation for mechanical systems with nonholonomic constraints

2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez
Keyword(s):  
Finite Number ◽  
Mechanical System ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Hamiltonian Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Hamilton Equations

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.

scholarly journals AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM BY INTRODUCING ADDITIONAL GENERALIZED KINEMATIC DEVICES

2021 ◽  
Vol 17 (4) ◽  
pp. 181-187
Author(s):  
Pavel Akimov ◽  
Leonid Lyakhovich
Keyword(s):  
Finite Number ◽  
Frequency Spectrum ◽  
Degrees Of Freedom ◽  
Mass Movement ◽  
Subsequent Paper ◽  
Elastic Plates ◽  
Natural Vibrations ◽  
Elastic Systems ◽  
The Creation ◽  
Generalized Constraint

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, for some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.

scholarly journals On Nonconservative Stability Problems of Elastic Systems With Slight Damping

1966 ◽  
Vol 33 (1) ◽  
pp. 125-133 ◽  
Author(s):  
G. Herrmann ◽  
I. C. Jong
Keyword(s):  
Degrees Of Freedom ◽  
Compressive Load ◽  
Viscous Damping ◽  
Two Degrees Of Freedom ◽  
Stability Problems ◽  
Damping Coefficients ◽  
Stability And Instability ◽  
Elastic Systems ◽  
Nonconservative Loading ◽  
Two Degree Of Freedom

A linear two-degree-of-freedom system with slight viscous damping and subjected to nonconservative loading is analyzed with the aim of studying the effects of damping on stability of equilibrium. It is found that, in such systems, multiple ranges of stability and instability may exist in a richer variety than in corresponding systems without damping. Further, for certain systems, instability either by divergence (static buckling) or by flutter may occur first as the compressive load increases, depending upon the ratio of the damping coefficients in the two degrees of freedom. It is shown finally that systems exist for which the destabilizing effect of slight viscous damping cannot be removed completely whatever the ratio of the (positive) damping coefficients.

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

Study of some rheological models with a finite number of degrees of freedom

2000 ◽  
Vol 19 (2) ◽  
pp. 277-307 ◽  
Author(s):  
Jérôme Bastien ◽  
Michelle Schatzman ◽  
Claude-Henri Lamarque
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Rheological Models

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

An Infinite Number of Laminagrams from a Finite Number of Radiographs

Radiology ◽  
1971 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Earl R. Miller ◽  
Edward M. MoCurry ◽  
Bernard Hruska
Keyword(s):  
Finite Number ◽  
Infinite Number
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