geometric formulation
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Robotica ◽  
2021 ◽  
pp. 1-11
Author(s):  
Matteo Russo ◽  
Marco Ceccarelli

Abstract In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.


2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Tyler Corbett

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.


Author(s):  
Youngsuk Hong ◽  
Ramy Rashad ◽  
Soocheol Noh ◽  
Taeyoon Lee ◽  
Stefano Stramigioli ◽  
...  

2021 ◽  
Author(s):  
James C. Sobotka ◽  
Yi-Der Lee ◽  
Joseph W. Cardinal ◽  
R. Craig McClung

Abstract This paper describes a new stress-intensity factor (SIF) solution for an external surface crack in a sphere that expands capabilities previously available for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations computed for the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located normal to the surface and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution accommodates spherical geometries with an exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressure vessels: uniform internal pressure on the interior surface, uniform tension on the crack plane, and uniform bending on the crack plane. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element analyses employed to calibrate terms in the WF formulation. A summary of preliminary verification efforts demonstrates the credibility of this solution against independent results from finite element analyses. We also compare results of this new solution against independent SIFs computed by finite element analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from finite element analyses. This paper summarizes ongoing efforts to improve and extend this solution, including formal verification and development of an internal surface crack model. Finally, we discuss the capabilities of this solution’s implementation in NASGRO® v10.0.


2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Tyler Corbett ◽  
Andreas Helset ◽  
Adam Martin ◽  
Michael Trott

Abstract We calculate the $$ \mathcal{O}\left({\left\langle {H}^{\dagger }H\right\rangle}^2/{\Lambda}^4\right) $$ O H † H 2 / Λ 4 corrections to LEP electroweak precision data using the geometric formulation of the Standard Model Effective Field Theory (SMEFT). We report our results in simple-to-use interpolation tables that allow the interpretation of this data set to dimension eight for the first time. We demonstrate the impact of these previously unknown terms in the case of a general analysis in the SMEFT, and also in the cases of two distinct models matched to dimension eight. Neglecting such dimension-eight corrections to LEP observables introduces a theoretical error in SMEFT studies. We report some preliminary studies defining such a theory error, explicitly demonstrating the effect of previously unknown dimension-eight SMEFT corrections on LEP observables.


Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 114
Author(s):  
Manuel Hohmann

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations.


2021 ◽  
Author(s):  
Youngsuk Hong ◽  
Ramy Rashad ◽  
Soocheol Noh ◽  
Taeyoon Lee ◽  
Stefano Stramigioli ◽  
...  

Abstract A geometric dynamic modeling framework for generic multirotor aerial vehicles (MAV), based on a modern Lie group formulation of classical screw theory, is presented. Our framework allows for a broad range of rotor-wing con gurations: any number of rotors can be attached in arbitrary con gurations to either the body or wings, with the rotors and wings also tiltable. Our framework takes into account all masses and inertias of the MAV body and rotors, and accounts for both rotor thrust forces and moments as well as external aerodynamic and other forces. Compared to existing methods, our Lie group framework possesses several practical advantages useful for applications ranging from design optimization to model identi cation and trajectory optimization: (i) the dynamic equations can be easily transformed to coordinates of any reference frame; (ii) kinematic and mass-inertial parameters can be easily factored from the dynamic equations; (iii) exact, closedform analytic derivatives of the dynamics with respect to the con guration variables are easily derived. We demonstrate our systematic modeling procedure on examples of xed-tilt, variable-tilt, and hybrid MAVs with wings.


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