Geodesic
Analysis of the pontoon fluctuations with a~seasonally changing parameter of stability on the astir surface of finite water depth
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 441-456

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It is shown that due to the periodic changes in metacentric heights of a pontoon on the astir surface of liquids in the sump of an open coal mine, the pontoon is capable to produce parametric pitching, both in the longitudinal and in the transverse directions. The equation, describing parametric pitching, is transformed to the Mathieu equation, whose factors depend both on the own frequencies and the pontoon floatability features on “calm water”, and on the frequency of fluctuation of a liquid, which, in turn, is defined by the sump size. The installed regularities between parameters, characterizing parametric pitching in the longitudinal and transverse directions, and areas of its instability are revealed. 
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     author = {S. V. Cherdantsev and N. V. Cherdantsev},
     title = {Analysis of the pontoon fluctuations with a~seasonally changing parameter of stability on the astir surface of finite water depth},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {441--456},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_4_a7/}
}
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S. V. Cherdantsev; N. V. Cherdantsev. Analysis of the pontoon fluctuations with a~seasonally changing parameter of stability on the astir surface of finite water depth. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 441-456. http://geodesic.mathdoc.fr/item/SJVM_2016_19_4_a7/