Erratum: Soluble models of rate processes in periodic systems with many degrees of freedom

1985 ◽  
Vol 32 (4) ◽  
pp. 2656-2656
Author(s):  
George H. Vineyard ◽  
James A. Krumhansl
Keyword(s):  
Degrees Of Freedom ◽  
Periodic Systems ◽  
Rate Processes

Soluble models of rate processes in periodic systems with many degrees of freedom

1985 ◽  
Vol 31 (8) ◽  
pp. 4929-4939 ◽  
Author(s):  
George H. Vineyard ◽  
James A. Krumhansl
Keyword(s):  
Degrees Of Freedom ◽  
Periodic Systems ◽  
Rate Processes

Localized Modes in Periodic Systems With Nonlinear Disorders

1997 ◽  
Vol 64 (4) ◽  
pp. 940-945 ◽  
Author(s):  
C. W. Cai ◽  
H. C. Chan ◽  
Y. K. Cheung
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Amplitude ◽  
Critical Value ◽  
Periodic Systems ◽  
Algebraic Equations ◽  
Localized Modes ◽  
Transformation Technique ◽  
Nonlinear Algebraic Equations ◽  
Coupling Stiffness ◽  
Localized Mode

The localized modes of periodic systems with infinite degrees-of-freedom and having one or two nonlinear disorders are examined by using the Lindstedt-Poincare (L-P) method. The set of nonlinear algebraic equations with infinite number of variables is derived and solved exactly by the U-transformation technique. It is shown that the localized modes exist for any amount of the ratio between the linear coupling stiffness kc and the coefficient γ of the nonlinear disordered term, and the nonsymmetric localized mode in the periodic system with two nonlinear disorders occurs as the ratio kc/γ, decreasing to a critical value depending on the maximum amplitude.

Forced Vibration Analysis for Damped Periodic Systems With One Nonlinear Disorder

1998 ◽  
Vol 67 (1) ◽  
pp. 140-147 ◽  
Author(s):  
H. C. Chan ◽  
C. W. Cai ◽  
Y. K. Cheung
Keyword(s):  
Degrees Of Freedom ◽  
Order Approximation ◽  
Structural Parameters ◽  
Harmonic Excitation ◽  
Zero Order ◽  
Periodic Systems ◽  
Pass Band ◽  
Driving Frequency ◽  
Attenuation Constant ◽  
Forced Vibration Analysis

The steady-state responses of damped periodic systems with finite or infinite degrees-of-freedom and one nonlinear disorder to harmonic excitation are investigated by using the Lindstedt-Poincare method and the U-transformation technique. The perturbation solutions with zero-order and first-order approximations, which involve a parameter n, i.e., the total number of subsystems, as well as the other structural parameters, are derived. When n approaches infinity, the limiting solutions are applicable to the system with infinite number of subsystems. For the zero-order approximation, there is an attenuation constant which denotes the ratio of amplitudes between any two adjacent subsystems. The attenuation constant is derived in an explicit form and calculated for several values of the damping coefficient and the ratio of the driving frequency to the lower limit of the pass band. [S0021-8936(00)01101-6]

scholarly journals Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

1997 ◽  
Vol 3 (4) ◽  
pp. 329-371
Author(s):  
Henryk Flashner ◽  
Ramesh S. Guttalu
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Mapping Method ◽  
Periodic Systems ◽  
Resonance Problem ◽  
Point Mapping ◽  
Analytical Stability ◽  
Functional Relations ◽  
Ground Resonance ◽  
The Stability

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

Das Experten-Novizen-Paradigma und die Vertrauenskrise in der Psychologie

2016 ◽  
Vol 23 (4) ◽  
pp. 131-140 ◽  
Author(s):  
Philip Furley ◽  
Karsten Schul ◽  
Daniel Memmert
Keyword(s):  
Degrees Of Freedom

Zusammenfassung. Das Ziel des vorliegenden Beitrages ist es anhand eines vielverwendeten Paradigmas in der Sportwissenschaft – dem Experten-Novizen-Vergleich – zu prüfen, ob die momentane Vertrauenskrise in der Psychologie ebenfalls die Sportpsychologie betreffen könnte. Anhand einer exemplarischen Studie zeigen wir, dass es innerhalb dieses Paradigmas zu kontroversen Befunden kommt, welche durch die vermuteten Ursachen der Vertrauenskrise (Researcher Degrees of Freedom, kleine Stichprobengrößen) erklärt sein könnten. Zusätzlich argumentieren wir, dass weitere Faktoren (Konfundierung, Stichprobengrößen, Rosenthal Effekt, Expertise-Definition) innerhalb dieses Paradigmas die Reproduzierbarkeit von Erkenntnissen in Frage stellen. Wir diskutieren mögliche Maßnahmen, wie die dargestellten Probleme des Experten-Novizen-Paradigmas in zukünftigen Forschungsarbeiten gelöst werden können.

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