Analytical Solutions for Averaged Equations of Optimal Orbit-to-orbit Transfer with a Thrust of Constant Magnitude in a Strong Gravity Field

Tsukamoto [N. Tsukamoto, Phys. Rev. D 95, 064035 (2017)] developed a method, which is an improvement over that of Bozza [V. Bozza, Phys. Rev. D 66, 103001 (2002)], for calculating light deflection angle in the strong gravity field of a spherically symmetric static spacetime. The method is directly applicable to the massless Ellis–Bronnikov wormhole (EBWH), while Bozza’s method is not applicable. We wish to show that it is still possible to obtain the same deflection angle by applying Bozza’s method but only in an indirect way, that is, first calculate the deflection by the parent massive EBWH and then take its massless limit.

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Feedback Optimal Control of Low-thrust Orbit Transfer in Central Gravity Field

International Journal of Advanced Computer Science and Applications ◽

10.14569/ijacsa.2013.040426 ◽

2013 ◽

Vol 4 (4) ◽

Author(s):

Ashraf H.

Keyword(s):

Optimal Control ◽

Gravity Field ◽

Low Thrust ◽

Orbit Transfer ◽

Feedback Optimal Control ◽

Low Thrust Orbit Transfer

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Optimum power-limited orbit transfer in strong gravity fields

10.2514/6.1964-666 ◽

1964 ◽

Cited By ~ 2

Author(s):

T. EDELBAUM

Keyword(s):

Orbit Transfer ◽

Strong Gravity ◽

Gravity Fields

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A Review of Russian Snow Avalanche Models—From Analytical Solutions to Novel 3D Models

Geosciences ◽

10.3390/geosciences10020077 ◽

2020 ◽

Vol 10 (2) ◽

pp. 77 ◽

Cited By ~ 1

Author(s):

Margarita Eglit ◽

Alexander Yakubenko ◽

Julia Zayko

Keyword(s):

Soviet Union ◽

Mathematical Models ◽

Turbulent Flows ◽

Analytical Solutions ◽

Numerical Study ◽

3D Models ◽

Snow Avalanches ◽

The Soviet Union ◽

Averaged Equations ◽

Mass Entrainment

The article is a review of mathematical models of snow avalanches that have been proposed since the middle of the 20th century and are still in use. The main attention is paid to the work of researchers from the Soviet Union and Russia, since many of their works were published only in Russian and are not widely available. Mathematical models of various levels of complexity for avalanches of various types—from dense to powder-snow avalanches—are discussed. Analytical solutions including formulas for the avalanche front speed are described. The results of simulations of the movement of avalanches are given that were used to create avalanche hazard maps. The last part of the article is devoted to constructing models of a new type, in which avalanches are considered as laminar or turbulent flows of non-Newtonian fluids, using the full (not depth-averaged) equations of continuum mechanics. The results of a numerical study of the effect of non-Newtonian rheology and mass entrainment on the avalanche dynamics are presented.

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