scholarly journals Gravity Models with Nonlinear Symmetry Realization

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 501
Author(s):  
Stanislav Alexeyev ◽  
Daniil Krichevskiy ◽  
Boris Latosh
Keyword(s):  
Early Universe ◽  
Degrees Of Freedom ◽  
Conformal Symmetry ◽  
Gravity Models ◽  
Target Space ◽  
Additional Symmetry ◽  
Non Linear

Validity of three gravity models with non-linear realization of conformal symmetry previously discussed in literature is addressed. Two models are found to be equivalent up to a change of coset coordinates. It was found that models contain ghost degrees of freedom that may be excluded by an introduction of an additional symmetry to the target space. One model found to be safe in early universe. The others found to lack spin-2 degrees of freedom and to have peculiar coupling to matter degrees of freedom.

An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2011 ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Element Analysis ◽  
Motion Direction ◽  
Form Analysis ◽  
Flexure Mechanism ◽  
Non Linear ◽  
Decoupled Motion ◽  
Motion Range ◽  
Parallel Kinematic ◽  
Cross Axis

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Theorical Analysis of Leakage in High Pressure Pipe Using Acoustic Emission Method

2012 ◽  
Vol 445 ◽  
pp. 917-922 ◽  
Author(s):  
Saman Davoodi ◽  
Amir Mostafapour
Keyword(s):  
High Pressure ◽  
Acoustic Emission ◽  
Degrees Of Freedom ◽  
Oil And Gas ◽  
Pipe Wall ◽  
Leak Detection ◽  
Stress Waves ◽  
Motion Equation ◽  
Non Linear ◽  
Acoustic Emission Test

Leak detection is one of the most important problems in the oil and gas pipelines. Where it can lead to financial losses, severe human and environmental impacts. Acoustic emission test is a new technique for leak detection. Leakage in high pressure pipes creates stress waves resulting from localized loss of energy. Stress waves are transmitted through the pipe wall which will be recorded by using acoustic sensor or accelerometer installed on the pipe wall. Knowledge of how the pipe wall vibrates by acoustic emission resulting from leakage is a key parameter for leak detection and location. In this paper, modeling of pipe vibration caused by acoustic emission generated by escaping of fluid has been done. Donnells non linear theory for cylindrical shell is used to deriving of motion equation and simply supported boundary condition is considered. By using Galerkin method, the motion equation has been solved and a system of non linear equations with 6 degrees of freedom is obtained. To solve these equations, ODE tool of MATLAB software and Rung-Kuta numerical method is used and pipe wall radial displacement is obtained. For verification of this theory, acoustic emission test with continues leak source has been done. Vibration of wall pipe was recorded by using acoustic emission sensors. For better analysis, Fast Fourier Transform (FFT) was taken from theoretical and experimental results. By comparing the results, it is found that the range of frequencies which carried the most amount of energy is same which expresses the affectivity of the model.

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

scholarly journals Hamiltonian formalism for nonlocal gravity models

2022 ◽  
Author(s):  
Pawan Joshi ◽  
Utkarsh Kumar ◽  
Sukanta Panda
Keyword(s):  
Ricci Tensor ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Lagrangian Formalism ◽  
Acceleration Of The Universe ◽  
Nonlocal Action ◽  
The Universe

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

NON-LINEAR GENERALIZATION OF THE GAUGE AMBIGUITIES OF THE LAGRANGIAN FORMALISM

1991 ◽  
Vol 06 (05) ◽  
pp. 737-748 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
MANUEL F. RAÑADA
Keyword(s):  
Degrees Of Freedom ◽  
Lagrangian Formalism ◽  
Two Degrees Of Freedom ◽  
Gauge Equivalence ◽  
General Properties ◽  
Non Linear

A generalization of the gauge equivalence of Lagrangians is developed. In this approach the different Lagrangians determine not only the same set of solutions but also the same energies. Some general properties are studied and then the case of velocity-free forces is considered. In particular we show the non-existence for n=2 (two degrees of freedom) of such equivalent Lagrangians and that when n=3 the only forces admitting such equivalent Lagrangians correspond to those deriving from central potentials.

Application of non-linear H∞ control to the Tetrabot robot manipulator

1998 ◽  
Vol 212 (6) ◽  
pp. 459-465 ◽  
Author(s):  
I Postlethwaite ◽  
A Bartoszewicz
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Industrial Robot ◽  
External Disturbances ◽  
Six Degrees Of Freedom ◽  
Control Scheme ◽  
Non Linear ◽  
Modelling Uncertainties ◽  
Real Robot ◽  
Robotic Application

In this paper, an application of a non-linear H∞ control law for an industrial robot manipulator is presented. Control of the manipulator motion is formulated into a non-linear H∞ optimization problem, namely optimal tracking performance in the presence of modelling uncertainties and external disturbances. Analytical solutions for this problem are implemented on a real robot. The robot under consideration is the six-degrees-of-freedom GEC Tetrabot. Investigations are made into the selection of weights for the H∞ controller and it is shown how different selections of weights affect the Tetrabot performance. The authors believe this to be the first robotic application of nonlinear H∞ control. Comparisons of the proposed control strategy with conventional proportional-derivative and proportional-integral-derivative controllers show favourable performance of the Tetrabot under the new non-linear H∞ control scheme.

scholarly journals Multiple choice of gauge generators and consistency of interactions

2014 ◽  
Vol 29 (31) ◽  
pp. 1450167 ◽  
Author(s):  
S. L. Lyakhovich ◽  
A. A. Sharapov
Keyword(s):  
Gauge Symmetry ◽  
Simple Model ◽  
Degrees Of Freedom ◽  
Multiple Choice ◽  
Gravity Models ◽  
Coupling Constant ◽  
Free Theory ◽  
Gauge Symmetries

It is usually assumed that any consistent interaction either deforms or retains the gauge symmetries of the corresponding free theory. We propose a simple model where an obvious irreducible gauge symmetry does not survive an interaction, while the interaction is consistent as it preserves the number of physical degrees of freedom. The model turns out admitting a less obvious reducible set of gauge generators which is compatible with the interaction and smooth in coupling constant. Possible application to gravity models is discussed.

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