Effect of Finite Rotations on Gyroscopic Sensing Devices

1958 ◽  
Vol 25 (2) ◽  
pp. 210-213
Author(s):  
L. E. Goodman ◽  
A. R. Robinson
Keyword(s):  
Angular Velocity ◽  
Three Dimensional ◽  
Time History ◽  
Simple Method ◽  
Finite Rotations ◽  
Actual Solution ◽  
History Of ◽  
Body Components ◽  
Guidance Systems ◽  
Three Body

Abstract The well-known noncommutativity of three-dimensional finite rotations has long been a curiosity in mechanics since, in actual solution of dynamical problems, the angular velocity, which is conveniently representable as a vector, plays a more natural role. In modern inertial guidance systems, however, the orientation of a body in space, i.e., a rotation, is of primary engineering interest. In this paper a simple method of determining orientation from the time history of three body components of angular velocity is developed by means of a new theorem in kinematics. As a special case of this theorem it is shown that a gyro subjected to a regime of rotations which returns it to the original space orientation will, in general, produce a residual signal. It will have experienced a nonzero and easily calculated mean angular velocity about its input axis. Some implications of the theorem for the design of inertial guidance systems and for the testing of gyros are discussed.

THREE‐DIMENSIONAL GRAVITY INSTABILITY DERIVED FROM TWO‐DIMENSIONAL SOLUTIONS

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 153-166 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Periodic Patterns ◽  
Numerical Work ◽  
Characteristic Distance ◽  
General Validity ◽  
Dimensional Gravity ◽  
History Of

The theory of three‐dimensional gravity instability of multilayers is developed with particular application to salt structures. It is shown that three‐dimensional solutions are immediately obtained without further numerical work from the solution of the corresponding two‐dimensional problem. Application to a number of typical three‐dimensional structures yields the characteristic distance between peaks and crests and shows that this distance does not differ significantly from the wavelength of the two‐dimensional solution. Various periodic patterns are examined corresponding to rectangular and hexagonal cells. The time history of nonperiodic structures corresponding to initial deviations from perfect horizontality is also derived. The method is applied to the three‐dimensional problem of generation of salt structures when the time‐history of sedimentation is taken into account with variable thickness and compaction of the overburden and establishes the general validity of the geological conclusions derived from the previous two‐dimensional treatment of the same problem (Biot and Odé, 1965). The present method of deriving three‐dimensional solutions, which is developed here in the special context of gravity instability, is valid for a wide variety of problems in theoretical physics.

scholarly journals In Situ, Doppler Radar, and Video Observations of the Interior Structure of a Tornado and the Wind–Damage Relationship

2013 ◽  
Vol 94 (6) ◽  
pp. 835-846 ◽  
Author(s):  
Joshua Wurman ◽  
Karen Kosiba ◽  
Paul Robinson
Keyword(s):  
Doppler Radar ◽  
Three Dimensional ◽  
Time History ◽  
Periodic Oscillation ◽  
Surface Flow ◽  
Near Surface ◽  
Direct Observations ◽  
Video Observations ◽  
History Of ◽  
Armored Vehicle

Direct observations of the winds inside a tornado were obtained with an instrumented armored vehicle, the Tornado Intercept Vehicle (TIV), and integrated with finescale mobile Doppler radar (Doppler on Wheels) data revealing, for the first time, the structure of the near-ground three-dimensional wind field in and around the core region of a strong tornado, and permitting comparison with conceptual models. Inward and upward spiraling near-surface flow, upward motion near the surface, and an axial downdraft aloft are documented, as well as a periodic oscillation in tornado intensity. Simultaneous video documentation of damage occurring during the tornado is related to the direct wind observations, permitting the first comparisons of the time history of damage to the time history of directly measured winds and a limited evaluation of the underlying assumptions and quantitative relationships in the enhanced Fujita (EF) scale.

3-D Numerical Simulation of Flow Around a Rectangular Cylinder

2003 ◽  
Author(s):  
Akira Rokugou ◽  
Atsushi Okajima ◽  
Takanori Isogawa
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Reynolds Numbers ◽  
Eddy Simulation ◽  
Eddy Viscosity Model ◽  
Side Ratio ◽  
Rectangular Cylinder ◽  
Large Eddy ◽  
History Of ◽  
Rectangular Cylinders

Three-dimensional numerical simulations of the flow around rectangular cylinders with depth-to-height ratios (side ratio) of 3 and 6 at various Reynolds numbers were carried out using the Large eddy simulation (LES), which employs the Smagorinsky eddy-viscosity model, a type of subgrid scale (SGS) model. Computed results compared well with experimental ones. The irregular fluctuation of aerodynamic forces can be simulated. The time history of the lift force corresponded well to the variation of flow pattern.

scholarly journals Influence of Disc Specimen Configuration on Its Three-Dimensional Dynamic Stress Balance

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Sheng Zhang ◽  
Bingxin Yu ◽  
Xiaojun Li ◽  
Longfei Wang ◽  
Xulong Zhang
Keyword(s):  
Dynamic Stress ◽  
Three Dimensional ◽  
Time History ◽  
Brazilian Disc ◽  
Disc Specimen ◽  
Loading Mode ◽  
Dimensional Finite Element ◽  
History Of ◽  
Three Dimensional Finite Element ◽  
Semicircular Bending

In order to investigate the dynamic stress balance of different configurations of rock specimens, three-dimensional finite element models of SHPB were established. Five types of configuration disc specimens with a diameter of 75 mm and a thickness of 30 mm were impacted at a speed of 5 m/s using a special-shaped bullet. The propagation laws of stress wave on the contact surface of the specimen-bar and the inside of the specimen were analyzed, and the time history of the stress balance factors at different positions of the specimen was obtained. The results show that the amplitudes of the transmitted waves corresponding to the five types of disc specimens with different configurations have obvious differences, and the stress propagation in the specimen has three-dimensional characteristics. According to the ease of achieving stress balance, the five configuration specimens are ordered by notched semicircular bending disc, flattened Brazilian disc, cracked straight-through flattened Brazilian disc, Brazilian disc, and cracked straight-through Brazilian disc specimen. Among them, only the first three configurations of the specimen reached the stress balance. The dynamic stress balance is affected by the disc loading mode, end contact conditions, the presence of prefabricated cracks, and disc thickness. In addition, as the disc loading end is a processed platform, it is beneficial to achieve stress balance. Prefabricated cracks are not conducive to achieving stress balance. The loading method of the notched semicircular bending disc is more conducive to achieving stress balance. This research has a certain guiding significance for selecting suitable specimen configuration and research methods to carry out rock dynamic fracture experiments.

Intermittency in free vibration of a cylinder beyond the laminar regime

2019 ◽  
Vol 870 ◽  
Author(s):  
Navrose ◽  
Sanjay Mittal
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Reynolds Numbers ◽  
Dominant Frequency ◽  
Laminar Regime ◽  
Mass Ratio ◽  
Aerodynamic Coefficients ◽  
History Of ◽  
Lock In ◽  
Intermittent Switching

Vortex-induced vibration of a circular cylinder that is free to move in the transverse ($Y$) and streamwise ($X$) directions is investigated at subcritical Reynolds numbers ($1500\lesssim Re\lesssim 9000$) via three-dimensional (3-D) numerical simulations. The mass ratio of the system for all the simulations is $m^{\ast }=10$. It is observed that while some of the characteristics associated with the $XY$-oscillation are similar to those of the $Y$-only oscillation (in line with the observations made by Jauvtis & Williamson (J. Fluid Mech., vol. 509, 2004, pp. 23–62)), notable differences exist between the two systems with respect to the transition between the branches of the cylinder response in the lock-in regime. The flow regime between the initial and lower branch is characterized by intermittent switching in the cylinder response, aerodynamic coefficients and modes of vortex shedding. Similar to the regime of laminar flow, the system exhibits a hysteretic response near the lower- and higher-$Re$ end of the lock-in regime. The frequency spectrum of time history of the cylinder response shows that the most dominant frequency in the streamwise oscillation on the initial branch is the same as that of the transverse oscillation.

Numerical Investigation of the Roll Decay of a Container Ship Moving With Forward Speed in Calm Water

2019 ◽  
Author(s):  
Adrian Lungu
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Numerical Approach ◽  
Container Ship ◽  
Angle Variation ◽  
Sst Model ◽  
Calm Water ◽  
History Of ◽  
Volume Method

Abstract In the present paper the roll damping decay is investigated for the KRISO Container Ship in various working conditions. For this purpose flow is simulated by solving numerically the unsteady three dimensional equations of fluid motion in which closure to the turbulence is achieved through the DES-SST model. The governing equations are solved by using the finite volume method and the free surface elevation is determined by using a VOF technique. Comparisons with the experimental data are provided to validate the numerical approach in terms of the time history of the roll angle variation for different roll motions and ship speeds.

A Study on the Interaction of Brain Impact With the Grounds of Different Material Types

2010 ◽  
Author(s):  
Parshuram Paka ◽  
Ghodrat Karami ◽  
Mariusz Ziejewski
Keyword(s):  
Shear Stress ◽  
Finite Elements ◽  
Material Properties ◽  
Three Dimensional ◽  
Viscoelastic Behavior ◽  
Time History ◽  
Human Head ◽  
Shear Stresses ◽  
History Of ◽  
The Brain

This paper proposes a parametric study of the response of brain, to human head impact with varied velocities as well as with the grounds of different material properties. The human head and its constituents are modeled using three-dimensional finite elements. The brain is made up of various elements that are modeled with a viscoelastic behavior. The ground is also assembled by finite elements. Five different velocities of impacts are considered based on realistic scenarios of human body falling due to gravity from five different heights. Three different materials for ground including wood, soil and rubber are considered. The simulation is run for a time history of 10ms after the incident. The intracranial coup pressure and shear stresses in the brain and various parts of the head are recorded. At the time of impact the peaks of the coup pressure and shear stress are observed to be proportional to the velocity of head and stiffness of the ground. Studies are conducted on the influence of the material of the impacting ground.

scholarly journals Simulation of Real Defect Geometry and Its Detection Using Passive Magnetic Inspection (PMI) Method

2018 ◽  
Vol 8 (7) ◽  
pp. 1147 ◽  
Author(s):  
Milad Mosharafi ◽  
SeyedBijan Mahbaz ◽  
Maurice Dusseault
Keyword(s):  
Reinforced Concrete ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Time History ◽  
Magnetic Behavior ◽  
Financial Risks ◽  
Reinforcing Steel ◽  
Reinforced Concrete Structure ◽  
Finite Element Software ◽  
History Of

Reinforced concrete is the most commonly used material in urban, road, and industrial structures. Quantifying the condition of the reinforcing steel can help manage the human and financial risks that arise from unexpected reinforced concrete structure functional failure. Also, a quantitative time history of reinforcing steel condition can be used to make decisions on rehabilitation, decommissioning, or replacement. The self-magnetic behavior of ferromagnetic materials is useful for quantitative condition assessment. In this study, a ferromagnetic rebar with artificial defects was scanned by a three-dimensional (3D) laser scanner. The obtained point cloud was imported as a real geometry to a finite element software platform; its self-magnetic behavior was then simulated under the influence of Earth’s magnetic field. The various passive magnetic parameters that can be measured were reviewed for different conditions. Statistical studies showed that 0.76% of the simulation-obtained data of the rebar surface was related to the defect locations. Additionally, acceptable coincidences were confirmed between the magnetic properties from numerical simulation and from experimental outputs, most noticeably at hole locations.

scholarly journals Flow Past Two Freely Rotatable Triangular Cylinders in Tandem Arrangement

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Shizhao Wang ◽  
Luoding Zhu ◽  
Xing Zhang ◽  
Guowei He
Keyword(s):  
Angular Velocity ◽  
Vortical Structure ◽  
Angular Acceleration ◽  
Time History ◽  
Vortical Structures ◽  
Spacing Ratio ◽  
History Of ◽  
Complicated Pattern ◽  
Cylinder Flow ◽  
Far Wake

In this paper we investigate the interaction of two freely rotatable triangular cylinders that are placed in tandem in a laminar flow. To study how the spacing between the two cylinders may influence the dynamic behavior of the cylinders and vortical structure of the flow, we have performed a series of numerical simulations of the two-cylinder-flow system. In all the simulations, the dimensionless moment of inertia and Reynolds number are fixed to 1.0 and 200, respectively. Four cases with the spacing ratio (L/D) of 2.0, 3.0, 4.0, and 5.0 are studied. With the increase of spacing, three different states of motion of the system are found. At L/D = 2.0, oscillatory rotation (swinging in both directions) is observed. At L/D = 3.0 both cylinders exhibit quasi-periodic autorotations. At L/D = 4.0 and 5.0, a more complicated pattern (irregular autorotation) is observed. For each case, the time history of angular velocity, the phase portrait (angular acceleration versus angular velocity,) and the spectra of the moments of forces on both cylinders are plotted and analyzed. The vortical structures in the near and far wake are visualized. Physical interpretations for various phenomenon observed are presented whenever possible.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

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