scholarly journals The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2047
Author(s):  
Rattanasak Hama ◽  
Sorin V. Sabau
Keyword(s):  
Arbitrary Direction ◽  
Surfaces Of Revolution ◽  
Killing Field ◽  
Navigation Problem ◽  
Rotational Surface ◽  
Randers Metric ◽  
Global Behaviour

In the present paper, we study the global behaviour of geodesics of a Randers metric, defined on Finsler surfaces of revolution, obtained as the solution of the Zermelo’s navigation problem. Our wind is not necessarily a Killing field. We apply our findings to the case of the topological cylinder R×S1 and describe in detail the geodesics behaviour, the conjugate and cut loci.

Analysis of Influence of Ephemeris-Time Information on Accuracy of Solving a Navigation Problem by Signals of GLONASS System

2020 ◽  
Vol 25 (5) ◽  
pp. 465-474
Author(s):  
V.O. Zhilinskiy ◽  
◽  
D.S. Pecheritsa ◽  
L.G. Gagarina ◽  
◽  
...  
Keyword(s):  
High Precision ◽  
Satellite Navigation ◽  
Satellite System ◽  
Navigation Systems ◽  
Navigation Problem ◽  
Satellite Navigation System ◽  
Study Results ◽  
Accuracy Of Measurements ◽  
Huge Impact ◽  
Time Information

The Global Navigation Satellite System has a huge impact on both the public and private sectors, including the social-economic development, it has many applications and is an integral part of many domains. The application of the satellite navigation systems remains the most relevant in the field of transport, including land, air and maritime transport. The GLONASS system consists of three segments and the operation of the entire system depends on functioning of each component, but primarily, the accuracy of measurements depends on the basis forming of the control segment and management, responsible for forming ephemeris-time information. In the work, the influence of ephemeris-time information on the accuracy of solving the navigation problem by the signals of the GLONASS satellite navigation system has been analyzed. The influence of both ephemeris information and the frequency information, and of the time corrections has been individually studied. The accuracy of the ephemeris-time information is especially important when solving the navigation problem by highly precise positioning method. For the analysis the following scenarios of the navigation problem solving have been formed: using high-precision and broadcast ephemeris-time information, a combination of broadcast (high-precision) ephemeris-time information, and high-precision (broadcast) satellite clock offsets and two scenarios with simulation of the calculation of the relative correction to the radio signal carrier frequency. Based on the study results it has been concluded that the contribution of the frequency-time corrections to the error of location determination is of the greatest importance and a huge impact on the error location, while the errors of the ephemeris information are insignificant

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

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