Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements

1979 ◽  
Vol 46 (4) ◽  
pp. 925-930 ◽  
Author(s):  
N. K. Mital ◽  
A. I. King
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Linear Acceleration ◽  
Field Measurements ◽  
Moving Frame ◽  
Accelerometer Data ◽  
Hypothetical Data

The angular acceleration of a rigid body with respect to a body-fixed (moving) frame can be reliably computed from nine acceleration field measurements. Noncommutativity of finite rotations causes computational problems during numerical integration to obtain the transformation matrix, especially when the rotation is three-dimensional and there are errors in the measured linear accelerations. A method based on the orientation vector concept is formulated and tested against hypothetical data. The rigid-body rotations computed from linear accelerometer data from impact acceleration tests are compared against those obtained from three-dimensional analysis of high speed movie films.

Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

scholarly journals A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Flight Control ◽  
Trajectory Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Dynamic Equations ◽  
Moving Frame ◽  
Moving Frames ◽  
Tracking Method ◽  
Tracking Process

The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

scholarly journals Saturated Ground Vibration Analysis Based on a Three-Dimensional Coupled Train-Track-Soil Interaction Model

2019 ◽  
Vol 9 (23) ◽  
pp. 4991 ◽  
Author(s):  
Li ◽  
Su ◽  
Kaewunruen
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Interaction Model ◽  
Ground Vibration ◽  
Field Measurements ◽  
Soil Conditions ◽  
Layered Soils ◽  
Train Track ◽  
Dynamic Interactions ◽  
Vibration Responses

A novel three-dimensional (3D) coupled train-track-soil interaction model is developed based on the multi-body simulation (MBS) principle and finite element modeling (FEM) theory using LS-DYNA. The novel model is capable of determining the highspeed effects of trains on track and foundation. The soils in this model are treated as saturated media. The wheel-rail dynamic interactions under the track irregularity are developed based on the Hertz contact theory. This model was validated by comparing its numerical results with experimental results obtained from field measurements and a good agreement was established. The one-layered saturated soil model is firstly developed to investigate the vibration responses of pore water pressures, effective and total stresses, and displacements of soils under different train speeds and soil moduli. The multi-layered soils with and without piles are then developed to highlight the influences of multi-layered soils and piles on the ground vibration responses. The effects of water on the train-track dynamic interactions are also presented. The original insight from this study provides a new and better understanding into saturated ground vibration responses in high-speed railway systems using slab tracks in practice. This insight will help track engineers to inspect, maintain, and improve soil conditions effectively, resulting in a seamless railway operation.

scholarly journals Vortex flow and cavitation in diesel injector nozzles

2008 ◽  
Vol 610 ◽  
pp. 195-215 ◽  
Author(s):  
A. ANDRIOTIS ◽  
M. GAVAISES ◽  
C. ARCOUMANIS
Keyword(s):  
High Speed ◽  
Fuel Injection ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Fuel Injector ◽  
Flowing Liquid ◽  
Injection Quantity ◽  
Dimensional Reconstruction ◽  
Real Size

Flow visualization as well as three-dimensional cavitating flow simulations have been employed for characterizing the formation of cavitation inside transparent replicas of fuel injector valves used in low-speed two-stroke diesel engines. The designs tested have incorporated five-hole nozzles with cylindrical as well as tapered holes operating at different fixed needle lift positions. High-speed images have revealed the formation of an unsteady vapour structure upstream of the injection holes inside the nozzle volume, which is referred to as ‘string-cavitation’. Computation of the flow distribution and combination with three-dimensional reconstruction of the location of the strings inside the nozzle volume has revealed that strings are found at the core of recirculation zones; they originate either from pre-existing cavitation sites forming at sharp corners inside the nozzle where the pressure falls below the vapour pressure of the flowing liquid, or even from suction of outside air downstream of the hole exit. Processing of the acquired images has allowed estimation of the mean location and probability of appearance of the cavitating strings in the three-dimensional space as a function of needle lift, cavitation and Reynolds number. The frequency of appearance of the strings has been correlated with the Strouhal number of the vortices developing inside the sac volume; the latter has been found to be a function of needle lift and hole shape. The presence of strings has significantly affected the flow conditions at the nozzle exit, influencing the injected spray. The cavitation structures formed inside the injection holes are significantly altered by the presence of cavitation strings and are jointly responsible for up to 10% variation in the instantaneous fuel injection quantity. Extrapolation using model predictions for real-size injectors operating at realistic injection pressures indicates that cavitation strings are expected to appear within the time scales of typical injection events, implying significant hole-to-hole and cycle-to-cycle variations during the corresponding spray development.

Computing Body Segment Trajectories in the Hybrid III Dummy Using Linear Accelerometer Data

1994 ◽  
Vol 116 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Rex T. Shea ◽  
David C. Viano
Keyword(s):  
High Speed ◽  
Angular Displacement ◽  
Angular Acceleration ◽  
Cost Savings ◽  
Accelerometer Data ◽  
Short Period ◽  
Planar Trajectory ◽  
Hybrid Iii ◽  
High Speed Film ◽  
New Generation

An analytical method was developed and tested using several mini-sled and Hyge sled tests to calculate the planar trajectory of a Hybrid III dummy head. Aimed at expediting the Hybrid III test analyses, it may provide an opportunity for cost savings through reduced hardware and manpower on film analyses. Transformation from the moving coordinate to the laboratory coordinate is based on the angular positions integrated from the derived angular accelerations. Gravitational correction of the linear accelerometers was found to be insignificant. The computed head trajectories were compared to the ones obtained from the high speed film images. Accuracy of the calculated head trajectory relies heavily on the accuracy of the computed angular acceleration. Strain-gaged accelerometers are not dependable at all times during an impact and an ill-behaved signal for a very short period may create a significant drift in computed displacement due to double integrations. Accuracy of the currently available accelerometers is not high enough for an angular displacement calculation. A new generation of accelerometers with higher accuracy, or an angular velocity sensor may provide more accurate angular displacement for trajectory analyses. The redundancy of the in-line accelerations helps improve the isolation of erroneous outputs and improve accuracy of the procedure.

scholarly journals Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

2021 ◽  
Vol 16 ◽  
pp. 73-84
Author(s):  
Maxim V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Fields ◽  
Characteristic Point ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Spatial Motion ◽  
Free Rigid Body

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

scholarly journals The Specification of Air-to-Air Combat Tactics Using UML Sequence Diagram

2021 ◽  
Vol 24 (6) ◽  
pp. 664-675
Author(s):  
Myunghwan Park ◽  
Jihyun Oh ◽  
Cheonyoung Kim ◽  
Hyeonju Seol
Keyword(s):  
Natural Language ◽  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sequence Diagram ◽  
Natural Languages ◽  
Extended Sequence ◽  
Air Combat ◽  
Current Sequence ◽  
Uml Sequence Diagram

Air force air-to-air combat tactics are occurring at a high speed in three-dimensional space. The specification of the tactics requires dealing with a quite amount of information, which makes it a challenge to accurately describe the maneuvering procedure of the tactics. The specification of air-to-air tactics using natural languages is not suitable because of the intrinsic ambiguity of natural languages. Therefore, this paper proposes an approach of using UML Sequence Diagram to describe air-to-air combat tactics. Since the current Sequence Diagram notation is not sufficient to express all aspects of the tactics, we extend the syntax of the Sequence Diagram to accommodate the required features of air-to-air combat tactics. We evaluate the applicability of the extended Sequence Diagram to air-to-air combat tactics using a case example, that is the manned-unmanned teaming combat tactic. The result shows that Sequence Diagram specification is more advantageous than natural language specification in terms of readability, conciseness, and accuracy. However, the expressiveness of the Sequence Diagram is evaluated to be less powerful than natural language, requiring further study to address this issue.

Experimental and numerical analyses of wedge effects on the rooster tail and porpoising phenomenon of a high-speed planing craft in calm water

2019 ◽  
Vol 233 (13) ◽  
pp. 4637-4652 ◽  
Author(s):  
Sayyed Mahdi Sajedi ◽  
Parviz Ghadimi ◽  
Mohammad Sheikholeslami ◽  
Mohammad A Ghassemi
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Scale Model ◽  
Test Cases ◽  
Planing Craft ◽  
Calm Water ◽  
Space Discretization ◽  
Good Agreement

This paper presents experimental and numerical investigation of stability and rooster tail of a mono-hull high-speed planing craft with a constant deadrise angle. Initially, a one-fifth scale model was tested in a towing tank, which showed porpoising phenomenon at 8 m/s (equal to the speed of sailing). Subsequently, two wedges of 5 and 10 mm heights, based on the boundary layer calculations, were mounted on the aft section of the planing hull. These wedges were shown to increase the lift at the aft section. These experiments were carried out at different speeds up to 10 m/s in calm water. The experimental results indicated that the installed wedges reduced the trim, drag, and the elapsed time for reaching the hump peak, and also eliminated the porpoising condition. All these test cases were also numerically simulated using Star CCM+ software. The free surface was modeled using the volume of fluid scheme in three-dimensional space. The examined planing craft had two degrees of freedom, and overset mesh technique was used for space discretization. The obtained numerical results were compared with experimental data and good agreement was displayed in the presented comparisons. Ultimately, the effect of the wedge on the rooster tail behind the planing craft was studied. The results of this investigation showed that by decreasing the trim at a constant speed, the height of the generated wake profile (rooster tail) behind the craft decreases, albeit its length increases.

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