Three- andN-body systems: An approach in terms of relative coordinates and momenta

1989 ◽  
Vol 39 (3) ◽  
pp. 1052-1058 ◽  
Author(s):  
R. J. Slobodrian
Keyword(s):  
Relative Coordinates

3D Scene Reconstruction Method in Relative Coordinates with Two Images from Non-Calibrated Video Cameras

2020 ◽  
Vol 25 (3) ◽  
pp. 265-276
Author(s):  
K.M. Shepilova ◽  
◽  
A.V. Sotnikov ◽  
A.V. Shipatov ◽  
Yu.V. Savchenko ◽  
...  
Keyword(s):  
Scene Reconstruction ◽  
Reconstruction Method ◽  
Video Cameras ◽  
Relative Coordinates ◽  
3D Scene ◽  
3D Scene Reconstruction

scholarly journals New Approach to the Planetary Theory

1979 ◽  
Vol 81 ◽  
pp. 69-72 ◽  
Author(s):  
Manabu Yuasa ◽  
Gen'ichiro Hori
Keyword(s):  
Perturbation Method ◽  
Canonical Form ◽  
Equations Of Motion ◽  
Disturbing Function ◽  
Averaging Principle ◽  
The Sun ◽  
Planetary Theory ◽  
New Approach ◽  
Canonical Perturbation ◽  
Relative Coordinates

A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).

Experimental and numerical investigation of railroad vehicle braking dynamics

2009 ◽  
Vol 223 (3) ◽  
pp. 255-267
Author(s):  
C Mellace ◽  
A P Lai ◽  
A Gugliotta ◽  
N Bosso ◽  
T Sinokrot ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Computer Algorithms ◽  
Coordinate Systems ◽  
State Equations ◽  
Relative Coordinates ◽  
Linear State ◽  
Cartesian Coordinate ◽  
Railroad Vehicle ◽  
Braking Dynamics

One of the important issues associated with the use of trajectory coordinates in railroad vehicle dynamic algorithms is the ability of such coordinates to deal with braking and traction scenarios. In these algorithms, track coordinate systems that travel with constant speeds are introduced. As a result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinates to be effectively used in modelling braking and traction dynamics. One of the objectives of this investigation is to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modelling braking and traction conditions. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of an arc length that represents the distance travelled by the body, and five relative coordinates that define the configuration of the body with respect to its track coordinate system. The independent non-linear state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinate systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The results obtained using the trajectory coordinates are compared with the results obtained using the absolute Cartesian-coordinate-based formulations, which allow modelling braking and traction dynamics. In addition to this numerical validation of the trajectory coordinate formulation in braking scenarios, an experimental validation is also conducted using a roller test rig. The comparison presented in this study shows a good agreement between the obtained experimental and numerical results.

scholarly journals Global Tropopause Altitudes in Radiosondes and Reanalyses

2018 ◽  
Author(s):  
Tao Xian ◽  
Cameron R. Homeyer
Keyword(s):  
Coordinate System ◽  
Lapse Rate ◽  
Vertical Resolution ◽  
Relative Coordinate ◽  
Relative Coordinates ◽  
Long Term Trends ◽  
The Tropics ◽  
Increasing Trends

Abstract. Accurate depictions of the tropopause and its changes are important for studies such as stratosphere-troposphere exchange and climate change.Here, the fidelity of primary lapse-rate tropopause altitudes and double tropopause frequencies in four modern reanalyses (ERA-Interim, JRA-55, MERRA-2, and CFSR) is examined using global radiosonde observations. In addition, long-term trends (1981–2015) in these tropopause properties are diagnosed in both the reanalyses and radiosondes. It is found that ERA-Interim, JRA-55, and CFSR reproduce observed tropopause altitudes with little bias and error comparable to the model vertical resolution, while MERRA-2 tropopause altitudes are biased 500–600 m high. All reanalyses underestimate the double tropopause frequency (up to 30 % lower than observed), with the largest biases found in JRA-55 and the smallest in CFSR. The underestimates in double tropopause frequency are primarily attributed to the coarse vertical resolution of the reanalyses. Significant increasing trends in both tropopause altitude (40–120 m per decade) and double tropopause frequency (≥ 3 % per decade) were found in both the radiosonde observations and reanalyses over the 35-year analysis period. ERA-Interim, JRA-55, and MERRA-2 broadly reproduce the patterns and signs of observed significant trends, while CFSR is inconsistent with the remaining datasets. These trends were diagnosed in both the native Eulerian coordinate system of the reanalyses and in a relative latitude coordinate system where the tropopause break (the discontinuity in tropopause altitude between the tropics and extratropics) was used as the reference latitude in each hemisphere. The tropopause break-relative coordinate facilitates the evaluation of tropopause behavior within the tropical and extratropical reservoirs and revealed significant differences in trend estimates compared to the traditional Eulerian analysis. Notably, increasing tropopause altitude trends were found to be of greater magnitude in tropopause break-relative coordinates and increasing double tropopause frequency trends were found to occur primarily poleward of the tropopause break in each hemisphere.

ACCURACY OF MEASURING SYSTEMS BASED ON LASER MODULES

2020 ◽  
pp. 44-53 ◽  
Author(s):  
V. E. Makhov ◽  
A. V. Emelyanov ◽  
A. I. Potapov ◽  
V. M. Petrushenko
Keyword(s):  
High Precision ◽  
Experimental Studies ◽  
Adaptive Algorithms ◽  
Measuring Systems ◽  
Precision Measuring ◽  
Relative Coordinates ◽  
Laser Module ◽  
Absolute Coordinates ◽  
Preliminary Selection

Measuring systems using the design of laser module beams on the surface of the object under study are considered. A technique is proposed for experimental studies of the brightness structure of the study of laser modules for their subsequent testing. Adaptive algorithms for determining the type of module and distance have been developed for determining the coordinates of light marks on the surface of controlled products, ensuring the accuracy and reliability of the measurement. The need for high-precision measuring systems to carry out their preliminary selection and calibration of laser modules according to the proposed method, taking into account the range of design of light marks, is shown. It is shown in the work that the accuracy of determining the relative coordinates in the trajectory of the light marks of laser modules at a distance of 5 m for plain surfaces of the observed objects can be several times higher (0,2…0,3 mm) of the accuracy of determining their absolute coordinates (»1 mm).

Zur Theorie der Kernrotationen

1961 ◽  
Vol 16 (11) ◽  
pp. 1119-1124
Author(s):  
Lothar Meichsner
Keyword(s):  
Additional Term ◽  
Heavy Nuclei ◽  
Energy Term ◽  
Max Planck ◽  
Rotating System ◽  
Additional Energy ◽  
Moments Of Inertia ◽  
Secondary Conditions ◽  
Rare Earth Nuclei ◽  
Relative Coordinates

Calculations of the moments of inertia of heavy nuclei without taking into account nucleonic interactions yielded values about twice the experimental ones. Such calculations were done at the Max-Planck-Institut für Physik for some rare-earth nuclei. A paper written by the author at the same institution offers a better agreement already if the nucleonic interactions again are neglected. It considers the fact that the nucleons do not move independently of one another in the rotating system of coordinates since introduction of Eulerian angles necessarily imposes secondary conditions on the relative coordinates of the nucleons. In consequence of this, an additional energy term, called „Zwangsenergie", occurs. After presenting the main results of the mentioned paper it is shown that this additional term alters energy differences entering the effective reciprocal moments of inertia in the sense of enlarging these moments, i. e., diminishing the effective moments of inertia, and that this contribution is not negligible. The presented theory differs from that of INGLIS by treating the rotations of the axially deformed potential quantum-mechanically instead by the help of a classical angular velocity.

Spatial Access Method for Flash Memory Embedded Systems

2011 ◽  
Vol 403-408 ◽  
pp. 4311-4317
Author(s):  
Ki Young Lee ◽  
Joung Joon Kim ◽  
Myung Jae Lim ◽  
Kyu Ho Kim ◽  
Jeong Lae Kim
Keyword(s):  
Embedded Systems ◽  
Spatial Data ◽  
Flash Memory ◽  
Operation Technique ◽  
Spatial Access ◽  
Compression Technique ◽  
Access Method ◽  
Memory Space ◽  
Relative Coordinates ◽  
Redundant Storage

This paper proposed an efficient spatial Access method, called MDR-Tree (Mbr compression and Delayed write operation based R-Tree), that uses the node compression technique and the delayed write operation technique for flash memory embedded systems. The node compression technique of MDR-Tree increased the utilization of flash memory space by compressing the MBR of spatial data using relative coordinates and MBR size. Moreover, the delayed write operation technique reduced the number of write operations in flash memory by temporarily storing spatial data in the buffer and by reflecting them in flash memory at once instead of reflecting the insert, update and delete of spatial data in flash memory for each operation. Especially, the utilization of buffer space was enhanced by preventing the redundant storage of the same spatial data in the buffer.

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