Reducing quasilinear systems to block triangular form

Tunitsky, Dmitry Vasilievich

doi:10.1070/sm2013v204n03abeh004307

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…These three equations are angular velocity calculated by coupling torque about this kind of liquid floated gyroscope. At the same time, (20) were substituted into the moment. To calculate the reduction of the angular velocity, the following are assumed:…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…The thermodynamic analysis of the dishing rotor gyroscope shows a continuous connection between the wellposed equation of differential thermodynamics and the continuum mechanics of the problems, because the dishing rotor gyroscope is filled with #3 industrial white oil; thus, a Godunov-type equation can be applied [20]…”

Section: Coupled Thermodynamic Theory Of the Gyroscope'smentioning

confidence: 99%

“…The Boltzmann equation of thermodynamics of the dishing rotor heat entropy in the growth equation is as follows [20]:…”

Section: Coupled Thermodynamic Theory Of the Gyroscope'smentioning

confidence: 99%

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Coupled Thermal Field of the Rotor of Liquid Floated Gyroscope

Wang

Yang

2015

Mathematical Problems in Engineering

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Inertial navigation devices include star sensor, GPS, and gyroscope. Optical fiber and laser gyroscopes provide high accuracy, and their manufacturing costs are also high. Magnetic suspension rotor gyroscope improves the accuracy and reduces the production cost of the device because of the influence of thermodynamic coupling. Therefore, the precision of the gyroscope is reduced and drift rate is increased. In this study, the rotor of liquid floated gyroscope, particularly the dished rotor gyroscope, was placed under a thermal field, which improved the measurement accuracy of the gyroscope. A dynamic theory of the rotor of liquid floated gyroscope was proposed, and the thermal field of the rotor was simulated. The maximum stress was inx, 1.4;y, 8.43; min 97.23; and max 154.34. This stress occurred at the border of the dished rotor at a high-speed rotation. The secondary flow reached 5549 r/min, and the generated heat increased. Meanwhile, the high-speed rotation of the rotor was volatile, and the dished rotor movement was unstable. Thus, nanomaterials must be added to reduce the thermal coupling fluctuations in the dished rotor and improve the accuracy of the measurement error and drift rate.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Coupled Thermodynamic Theory Of the Gyroscope'smentioning

confidence: 99%

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Coupled Thermal Field of the Rotor of Liquid Floated Gyroscope

Wang

Yang

2015

Mathematical Problems in Engineering

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“…В работе [7] изучается приводимость к блочно-треугольному виду квазилинейных систем общего вида с двумя независимыми переменными. Основные результаты формулируются и доказываются в терминах, аналогичных использованным в статье [3].…”

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“…Основные результаты формулируются и доказываются в терминах, аналогичных использованным в статье [3]. Частным случаем полученных в [7] результатов являются леммы 4.3, 4.4 и 4.5 настоящей статьи. Эти леммы играют весьма важную вспомогательную роль и существенно используются и в § 6 при доказательстве основных результатов, и в § 5 для иллюстрации этих результатов на примере системы уравнений газовой динамики.…”

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Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction

Туницкий¹,

Tunitsky²

2015

Известия Российской академии наук. Серия математическая

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Разделение систем гидродинамического типа на блочно-треугольно взаимодействующие подсистемы Статья посвящена системам n неоднородных уравнений гидродинамического типа с двумя независимыми переменными. Для таких систем имеет место восходящая к Риману геометрическая формализация, позволяющая поставить в соответствие системе гидродинамического типа векторное поле и поле линейных операторов, действующее на соответствующем касательном расслоении. В терминах этих полей получен ряд признаков разделения неоднородных систем гидродинамического типа на блочно-треугольно взаимодействующие подсистемы. Эти признаки дополняют известные результаты О. И. Богоявленского о разделении однородных систем гидродинамического типа на невзаимодействующие подсистемы. Библиография: 16 наименований. Ключевые слова: системы гидродинамического типа, невзаимодействующие подсистемы, блочно-треугольно взаимодействующие подсистемы, тензор Нейенхейса.

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On the decoupling problem of general quasilinear first order systems in two independent variables

Gorgone

Oliveri

Speciale

2017

Journal of Mathematical Analysis and Applications

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The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous systems. Necessary and sufficient conditions for the partial or full decoupling of the systems at hand are provided. The conditions involve the properties of eigenvalues and eigenvectors of the coefficient matrix, and provide the differential constraints whose integration leads to the decoupling transformation. Some applications of physical interest are also given.

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Reducing quasilinear systems to block triangular form

Cited by 3 publications

References 4 publications

Coupled Thermal Field of the Rotor of Liquid Floated Gyroscope

Coupled Thermal Field of the Rotor of Liquid Floated Gyroscope

Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction

On the decoupling problem of general quasilinear first order systems in two independent variables

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