Topic
Degrees of freedom
About: Degrees of freedom is a research topic. Over the lifetime, 6449 publications have been published within this topic receiving 124878 citations.
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TL;DR: The standard model of particle physics is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm as discussed by the authors.
Abstract: Particle physicists have spent much of this century grappling with one basic question in various forms: what are the fundamental degrees of freedom needed to describe nature, and what are the laws that govern their dynamics? First molecules, then atoms, then “elementary particles” such as protons and neutrons all have been revealed to be composite objects whose constituents could be studied as more fundamental degrees of freedom. The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom. The standard model is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm, far beyond our abilities to measure in the laboratory.
The study of motion and gravity also has undergone several revisions during this century. Reconciling the Newtonian theory of motion with the experimentally observed constancy of the speed of light required the introduction of special relativity, which quite remarkably insists that space and time are intimately related, much as different faces of the same …
2,812 citations
01 Jun 1965
TL;DR: In this article, the authors describe a six-degree-of-freedom control with six motors, each having a ground abutment, for simulating flight conditions in the training of pilots.
Abstract: This paper describes a mechanism which has six degrees of freedom, controlled in any combination by six motors, each having a ground abutment. It is considered that by its particular arrangement, this mechanism may form an elegant design for simulating flight conditions in the training of pilots. Unlike most simulators, it has no fixed axes relative to the ground, and therefore within the limits of amplitude of the design it can truly simulate the conditions of banking by carrying the simulation of control surfaces into the axes of the new attitude.Variations in control arrangements are described and their respective design merits considered.Other possible uses for this mechanism are mentioned, including automation of production.
2,341 citations
TL;DR: In this article, a general procedure for simplifying chemical kinetics is developed, based on the dynamical systems approach, in contrast to conventional reduced mechanisms no information is required concerning which reactions are to be assumed to be in partial equilibrium nor which species are assumed to remain in steady state.
1,492 citations
TL;DR: A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed and a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals.
Abstract: A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N2) degrees of freedom using only N physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input-minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.
1,478 citations
TL;DR: An operational meaning to ” controlled” and ”uncontrolled” is given and a method of analysis through which hypotheses about controlled and uncontrolled degrees of freedom can be tested is described, finding that, for the task of sit-to-stand, the position of the center of mass in the sagittal plane was controlled.
Abstract: The degrees of freedom problem is often posed by asking which of the many possible degrees of freedom does the nervous system control? By implication, other degrees of freedom are not controlled. We give an operational meaning to "controlled" and "uncontrolled" and describe a method of analysis through which hypotheses about controlled and uncontrolled degrees of freedom can be tested. In this conception, control refers to stabilization, so that lack of control implies reduced stability. The method was used to analyze an experiment on the sit-to-stand transition. By testing different hypotheses about the controlled variables, we systematically approximated the structure of control in joint space. We found that, for the task of sit-to-stand, the position of the center of mass in the sagittal plane was controlled. The horizontal head position and the position of the hand were controlled less stably, while vertical head position appears to be no more controlled than joint motions.
1,333 citations