Applications of the Global Coordinate System

Author(s):  
Yves Balasko

The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ‎, ω‎) where b = φ‎((ρ‎, ω‎) = (ρ‎, ρ‎ · ρ‎1, …, ρ‎ · ρ‎m); and (2) the determination of the location of the equilibrium (ρ‎, ω‎) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ‎, ω‎), there are different ways of representing the equilibrium (ρ‎, ω‎) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.

2020 ◽  
Vol 962 (8) ◽  
pp. 24-37
Author(s):  
V.E. Tereshchenko

The article suggests a technique for relation global kinematic reference system and local static realization of global reference system by regional continuously operated reference stations (CORS) network. On the example of regional CORS network located in the Novosibirsk Region (CORS NSO) the relation parameters of the global reference system WGS-84 and its local static realization by CORS NSO network at the epoch of fixing stations coordinates in catalog are calculated. With the realization of this technique, the main parameters to be determined are the speed of displacement one system center relativly to another and the speeds of rotation the coordinate axes of one system relatively to another, since the time evolution of most stations in the Russian Federation is not currently provided. The article shows the scale factor for relation determination of coordinate systems is not always necessary to consider. The technique described in the article also allows detecting the errors in determining the coordinates of CORS network in global coordinate system and compensate for them. A systematic error of determining and fixing the CORS NSO coordinates in global coordinate system was detected. It is noted that the main part of the error falls on the altitude component and reaches 12 cm. The proposed technique creates conditions for practical use of the advanced method Precise Point Positioning (PPP) in some regions of the Russian Federation. Also the technique will ensure consistent PPP method results with the results of the most commonly used in the Russian Federation other post-processing methods of high-precision positioning.


Author(s):  
Yves Balasko

This chapter addresses the global structure of the equilibrium manifold E. It starts by motivating these global properties for their economic interest. These global properties can be of a topological nature like pathconnectedness, simple connectedness, and contractibility. They can also take a more practical form like the existence of global coordinate systems for the points of the equilibrium manifold in the same way the points at the surface of the earth can be located through their longitude and latitude. The chapter identifies an important subset of the equilibrium manifold, the set of no-trade equilibria. This enables us to uncover the remarkable structure of the equilibrium manifold as a collection of linear spaces parameterized by the no-trade equilibria. This remarkable structure is then applied to define a global coordinate system for the equilibrium manifold.


1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.


1990 ◽  
Vol 141 ◽  
pp. 99-110
Author(s):  
Han Chun-Hao ◽  
Huang Tian-Yi ◽  
Xu Bang-Xin

The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5.


Author(s):  
Susan M. Moore ◽  
Mary T. Gabriel ◽  
Maribeth Thomas ◽  
Jennifer Zeminski ◽  
Savio L.-Y. Woo ◽  
...  

Knowledge of joint kinematics contributes to the understanding of the function of soft tissue restraints, injury mechanisms, and can be used to evaluate surgical repair techniques. (Tibone, McMahon et al. 1998; Karduna, McClure et al. 2001; Abramowitch, Papageorgiou et al. 2003) Previous studies have measured joint kinematics using a variety of non-invasive methods that include: optical tracking, magnetic tracking, and mechanical linkage systems. (Rudins, Laskowski et al. 1997; Apreleva, Hasselman et al. 1998; Gabriel, Wong et al. 2004) These measurement devices report kinematics of rigid bodies with respect their own global coordinate system. However, it is often useful to understand these kinematics in terms of a coordinate system whose axes coincide with the degrees of freedom of each specific joint (anatomical coordinate systems). Once the kinematics are obtained with respect to the global coordinate system of the measurement device, the joint kinematics can be calculated with respect to anatomical coordinate systems if the relationship between the measurement device and the anatomical coordinate systems are known. Although the accuracy of these kinematic measurement devices is provided by the manufacturer, the effect of their accuracy on joint kinematics reported with respect to anatomical coordinate systems must be determined. (Panjabi, Goel et al. 1982; Crisco, Chen et al. 1994) For example, small errors in orientation of the measurement system could lead to large errors in position for an anatomical coordinate system located at some distance away. As researchers report joint kinematics with respect to the anatomical coordinate systems, understanding the errors produced by one’s measurement device with respect to the anatomical coordinate systems is necessary. Further, a great deal of interest exists for studying knee joint kinematics. (Sakane, Livesay et al. 1999; Lephart, Ferris et al. 2002; Ford, Myer et al. 2003) Within our research center our goal is to collect knee joint kinematics of a cadaver and reproduce them with respect to the anatomical coordinate systems using robotic technology. Therefore, the objective of this study was to determine the effect of the accuracy of three measurement devices (optical tracking device-OptoTrak® 3020, magnetic tracking device-Flock of Birds®, instrumented spatial linkage-EnduraTec Corp.) on knee joint kinematics reported with respect to an anatomical coordinate system.


Author(s):  
Danilo Machado Lawinscky da Silva ◽  
Rodrigo Almeida Bahiense ◽  
Breno Pinheriro Jacob ◽  
Fernando Gomes da Silva Torres ◽  
Antonio Roberto Medeiros ◽  
...  

Conventional offshore pipeline installation operations in Brazil have been performed in an S-Lay procedure employing the BGL-1 barge, owned by Petrobras. However, this procedure has some limits, and may not be feasible in some particular scenarios. Therefore, the objective of this work is to present the numerical simulation of an alternative pipeline installation procedure. This procedure basically consists of performing the pipeline assembly on shore, and deflecting it to the sea using a tug boat. The numerical simulations employ the SITUA-Prosim computational tool, which is able to incorporate the correct definition of the seabed and shore from bathymetric curves. An actual pipeline installation by this lateral deflection procedure is analyzed and discussed. The characterization of the procedure passes through the determination of the better velocity and direction of the tug boat in order to minimize the efforts on the pipeline (especially due to the curvatures).


1997 ◽  
Vol 19 (5) ◽  
pp. 559
Author(s):  
G. MacFarlane ◽  
D. Scheller ◽  
D. Ersfeld ◽  
B. Fox ◽  
J. Obritsch ◽  
...  

2001 ◽  
Vol 17 (2) ◽  
pp. 173-180 ◽  
Author(s):  
Adrienne E. Hunt ◽  
Richard M. Smith

Three-dimensional ankle joint moments were calculated in two separate coordinate systems, from 18 healthy men during the stance phase of walking, and were then compared. The objective was to determine the extent of differences in the calculated moments between these two commonly used systems and their impact on interpretation. Video motion data were obtained using skin surface markers, and ground reaction force data were recorded from a force platform. Moments acting on the foot were calculated about three orthogonal axes, in a global coordinate system (GCS) and also in a segmental coordinate system (SCS). No differences were found for the sagittal moments. However, compared to the SCS, the GCS significantly (p < .001) overestimated the predominant invertor moment at midstance and until after heel rise. It also significantly (p < .05) underestimated the late stance evertor moment. This frontal plane discrepancy was attributed to sensitivity of the GCS to the degree of abduction of the foot. For the transverse plane, the abductor moment peaked earlier (p < .01) and was relatively smaller (p < .01) in the GCS. Variability in the transverse plane was greater for the SCS, and attributed to its sensitivity to the degree of rearfoot inversion. We conclude that the two coordinate systems result in different calculations of nonsagittal moments at the ankle joint during walking. We propose that the body-based SCS provides a more meaningful interpretation of function than the GCS and would be the preferred method in clinical research, for example where there is marked abduction of the foot.


Author(s):  
I.E. Semenov

The results of the experimental studies on determination of the Muni—Rivlin coefficients arising under plane strain of reinforced polyurethane sample are described.


2015 ◽  
Vol 8 (4) ◽  
pp. 491-506
Author(s):  
J. A. DE CARVALHO NETO ◽  
L. A. C. M. VELOSO

AbstractThe knowledge on the active moving load of a bridge is crucial for the achievement of the information on the behavior of the structure, and thus foresee maintenance, repairs and better definition of the logistics of its active vehicles. This paper presents the development of the algorithms for the application of the Bridge-Weigh In Motion (B-WIM) method created by Moses for the weighing of trains during motion and also for the characterization of the rail traffic, allowing the obtainment of information like passage's train velocity and number and spacing of axles, eliminating the dynamic effect. There were implemented algorithms for the determination of the data referring to the geometry of the train and its loads, which were evaluated using a theoretical example, in which it was simulated the passage of the train over a bridge and the loads of its axles were determined with one hundred percent of precision. In addition, it was made a numerical example in finite elements of a reinforced concrete viaduct from the Carajás' Railroad, in which the developed system reached great results on the characterization and weighing of the locomotive when the constitutive equation of the Brazilian Standards was substituted by the one proposed by Collins and Mitchell.


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