axis passing
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Author(s):  
V. Rovenski ◽  
P. Walczak

We introduce and study certain deformation of Minkowski norms in [Formula: see text] determined by a set of [Formula: see text] linearly independent 1-forms and a smooth positive function of [Formula: see text] variables. In particular, the deformation of a Euclidean norm [Formula: see text] produces a Minkowski norm defined in our recent work; its indicatrix is a rotation hypersurface with a [Formula: see text]-dimensional axis passing through the origin. For [Formula: see text], our deformation generalizes the construction of [Formula: see text]-norms which form a rich class of “computable” Minkowski norms and play an important role in Finsler geometry. We characterize such pairs of a Minkowski norm and its image that Cartan torsions of the two norms either coincide or differ by a [Formula: see text]-reducible term. We conjecture that for [Formula: see text] any Minkowski norm can be approximated by images of a Euclidean norm.


Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 191
Author(s):  
Ji-Huan He ◽  
Tarek S. Amer ◽  
Shimaa Elnaggar ◽  
Abdallah A. Galal

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.


2021 ◽  
Vol 26 (1) ◽  
pp. 14-22
Author(s):  
Ryszard Filipowski ◽  
Józef Zawora

A computer program for calculating cylinder parameters was developed based on a measurement strategy of five circles arranged along the cylinder axis. The parameters calculated by the program are: cylinder diameter, axis of inclination of the cylinder axis to the reference plane, deviations from the least squares reference cylinder (LSCY), the axis passing through the centers of the outermost measurement circles. The graphics of deviation from the cylinder dimension is shown in the Auto CAD system using the script command. The developed program complements the CMM software.


Author(s):  
Ray J. Butcher ◽  
Andrew P. Purdy

In the title compound, [Al2Br4(CH2)(C4H10O)2], the molecule lies on a crystallographic twofold axis passing through the bridging C atom. Each AlIII atom is four-coordinate, being bonded to two bromide ions, bridging the CH2 group as well as the oxygen atom of a diethyl ether ligand in a slightly distorted tetrahedral arrangement with angles ranging from 101.52 (8) to 116.44 (5)°. The Al—CH2—Al angle, 118.4 (2)°, is the smallest observed for a structure where this moiety is not part of a ring. In the crystal, weak C—H...Br interactions, characterized as R 2 2(12) rings, link the molecules into ribbons in the [101] direction. The title compound is monomeric and coordinatively saturated in the solid state, as each aluminum is four-coordinate, but in solution the ether molecules from either or both Al atoms can dissociate, and would be expected to rapidly exchange, and this is supported by NMR data.


2021 ◽  
Vol 11 (4) ◽  
pp. 1869
Author(s):  
Jesús Aguilar-Jiménez ◽  
Juan Manuel García-Guerrero ◽  
Juan José Jorquera-Lucerga

A diagonal arch bridge (DAB) is a particular case of arch bridge where the arch is rotated about a vertical axis passing through its crown so that each springing lies on a different side of the deck. A perpendicular arch bridge (PAB) is a particular case of DAB where the arch is rotated so that the arch plan is perpendicular to the deck axis. This paper includes a table of built bridges since 1989 and outlines the historical evolution of this type of bridge. Two main trends can be distinguished—one approach is focused on structural efficiency and the other is based on making aesthetics prevail, which often leads to structurally inefficient solutions. The main geometrical parameters are identified and the effect of the angle of rotation about a vertical axis is studied. Design constraints, such as the clearance requirements, are highlighted. In addition, the main structural systems, such as out-of-plane behavior, are identified and qualitatively studied, as an orientation for designers and a first step in future studies.


2021 ◽  
Vol 13 (2) ◽  
pp. 168781402199811
Author(s):  
Wu Xianfang ◽  
Du Xinlai ◽  
Tan Minggao ◽  
Liu Houlin

The wear-ring abrasion can cause performance degradation of the marine centrifugal pump. In order to study the effect of front and back wear-ring clearance on a pump, test and numerical simulation were used to investigate the performance change of a pump. The test results show that the head and efficiency of pump decrease by 3.56% and 9.62% respectively at 1.0 Qd due to the wear-ring abrasion. Under 1.0 Qd, with the increase of the front wear-ring the vibration velocity at pump foot increases from 0.4 mm/s to 1.0 mm/s. The axis passing frequency (APF) at the measuring points increases significantly and there appears new characteristic frequency of 3APF and 4APF. The numerical simulation results show that the front wear-ring abrasion affects the flow at the inlet of the front chamber of the pump and impeller passage. And the back wear-ring abrasion has obvious effect on the flow in the back chamber of the pump and impeller passage, while the multi-malfunction of the front wear-ring abrasion and back wear-ring abrasion has the most obvious effect on the flow velocity and flow stability inside pump. The pressure pulsation at Blade Passing Frequency (BPF) of the three schemes all decrease with the increase of the clearance.


Author(s):  
Giovanni Paolo Galdi ◽  
Giusy Mazzone

Consider the  motion of the the coupled system, $\mathscr S$, constituted by a (non-necessarily symmetric) top, $\mathscr B$, with an interior cavity, $\mathscr C$, completely filled up with a Navier-Stokes  liquid, $\mathscr L$. A particular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when $\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as a whole rigid body, spins with a constant angular velocity $\bar{\V\omega}$ around a vertical axis passing through its center of mass $G$ in its highest position ({\em upright spinning top}). We then provide a completely characterization of the nonlinear stability of $\bar{\sf s}$ by showing, roughly speaking, that $\bar{\sf s}$ is stable if and only if $|\bar{\V\omega}|$ is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration.


2020 ◽  
pp. 109-115
Author(s):  
Валентин Иванович Козлов ◽  
Татьяна Юрьевна Цветкова

Целью настоящего аналитического исследования является решение вопроса о биомеханике подвижности ребер при дыхательных экскурсиях грудной клетки и возможности участия в этих движениях так называемых мышц, поднимающих ребра. В большинстве современных руководств по анатомии функция этих мышц освещается в соответствии с их названием. Однако в более ранних работах высказывались сомнения об участии этих мышц в поднимании ребер. Анатомобиомеханические особенности соединения ребер грудной клетки не допускают изменения их положения относительно позвоночного столба и смещение их как в краниальном направлении (т. е. поднятие ребер), так и в каудальном направлении (т. е. опускание ребер). При дыхании как истинные, так и ложные ребра, постоянно сохраняют свое положение относительно позвоночного столба, к которому каждое ребро фиксируется малоподвижными суставами в двух точках. Допустимо только вращение ребер вокруг оси, косо проходящей вдоль шейки ребра. Однако благодаря искривленной форме ребер при их вращении изменяется пространственное положение тела и грудинного конца ребер. Поскольку название mm. levatores costarum не соответствует их функции как поднимателей и даже как вращателей ребер, то представляется оправданным изменение их номенклатурного названия. Исходя из реальных анатомо-биомеханических особенностей этих мышц, их следует причислить к мышцам, действующим на позвоночный столб, которые обеспечивают его ротацию и разгибание. Этим мышцам более присуще название реберно-поперечные мышцы (mm. costotransversales). В этом названии отражена их наиболее вероятная функция как вращателей и разгибателей позвоночного столба в грудном отделе. Objective - to solve the problem of the biomechanics of the mobility of the ribs during thoracic respiratory excursion and the possibility of participation of the so-called mm. levatores costarum in these movements. In most modern anatomy guidelines, the function of these muscles is covered according to their name. However, in earlier works doubts were expressed about the involvement of these muscles in lifting the ribs. Both true and false ribs can neither raise nor lower during respiratory excursions of the chest due to the anatomical and biomechanical properties of their articulations in the chest. During chest expansion and compression, the ribs constantly maintain their original position relative to the vertebral column, to which each rib is fixed by tight joints at two points. Therefore, the only possible movement is rotation of the ribs around oblique axis passing along the rib neck. The curved shape of the ribs is responsible for the change in space position of the body and the sternal end of the ribs during their rotation. As far as the name mm. levatores costarum do not correspond to their function as lifters and even as rotators of ribs, it seems justified to change their nomenclature name. Based on the real anatomical and biomechanical peculiarities of these muscles, they should be ranked with the muscles which are responsible for rotation and extension of the spinal column. The name costotransverse muscles (mm. costotransversales) are more applicable for these muscles. This name reflects their most likely function as rotators and extensors of the spinal column in the thoracic region.


Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1617
Author(s):  
Polidor Bratu

The dynamic model of the system of bodies with elastic connections substantiates the conceptual basis for evaluating the technological vibrations of the compactor roller as well as of the parameters of the vibrations transmitted from the vibration source to the remainder of the equipment components. In essence, the multi-body model with linear elastic connections consists of a body in vertical translational motion for vibrating roller with mass m1, a body with composed motion of vertical translation and rotation around the transverse axis passing through its weight center for the chassis of the car with mass m and the moment of mass inertia J and a body of mass m’ representing the traction tire-wheel system located on the opposite side of the vibrating roller. The study analyzes the stationary motion of the system of bodies that are in vibrational regime as a result of the harmonic excitation of the m mass body, with the force F(t)= m0rω2sinωt, generated by the inertial vibrator located inside the vibrating roller. The vibrator is characterized by the total unbalanced m0 mass in rotational motion at distance r from the axis of rotation and the angular velocity or circular frequency ω.


Author(s):  
M. L. Tazir ◽  
N. Seube

Abstract. Three-dimensional LiDAR rangefinders are increasingly integrated into unmanned aerial vehicles (UAV), due to their direct access to 3D information, their high accuracy and high refresh rate, and their tendency to be lightweight and cheaper. However, all commercial LiDARs can only offer a limited vertical resolution. To cope with this problem, a solution can be to rotate the LiDAR on an axis passing through its center, adding an additional degree of freedom and allowing more overlap, which significantly enlarges the sensor scope and allows having a complete spherical field of view (FOV). In this paper, we explore this solution in detail for drone’s context, while making comparisons between the rotating and fixed configurations for a Multi-Layers LiDAR (MLL) of type Velodyne Puck Lite. We investigate its impact on the LiDAR Odometry (LO) process by comparing the resulting trajectories with the data of the two configurations, as well as, qualitative comparisons, of the resulting maps.


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