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We consider the problem of finding the generalized potential function V = U
i(q
1, q
2,..., q
n)q
i + U(q
1, q
2,...;q
n) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U
1, U
2,...;, U
n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M
2 we obtain, for potential function U(q
1, q
2), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council. 相似文献
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Günay Erpul Donald Gabriels Melis Özge Pınar Çağlar Sagun Wim Cornelis 《地球表面变化过程与地形》2021,46(14):2870-2883
The effects of wind-driven rain (WDR) on sand detachment were studied under various raindrop obliquities. Results suggested a significant reduction in compressive stress on sand surfaces for a two-dimensional experimental set-up in a wind tunnel. During experiments, sand particles in splash cups were exposed to both wind-free rain (WFR) and WDR driven by horizontal winds of 6.4, 8.9 and 12.8 m s−1 and rainfall intensities of 50, 60, 75 and 90-mm h−1 to assess the sand detachment rate (D, in g m−2 s−1). The effects of sand moisture state (dry and wet) on the detachment of different-sized particles (0.20–0.50 and 0.50–2.00 mm, respectively) were also tested. Factorial analysis of variance showed that shear and compressive stress components evaluated by horizontal and vertical kinetic energy flux terms (KEx and KEy, respectively, in J m−2 s−1) along with their vector sum (KEr, in J m−2 s−1) explained the variation in D. Neither sand size nor sand moisture was statistically significant alone although binary interactions of KEr, KEx and KEy with the sand size and three-way interaction of KEx, sand size and moisture were statistically significant. These results can be explained by size-dependent variation in sand compressibility and surface friction related to the total stress field developed by a given partition of shear and compressive stresses of wind-driven oblique raindrops (KEx/KEy). Further analysis of the variation of the unit sand detachment rate (Du = D/KEr = g J−1) with rain inclination (α, in degrees) better revealed the effect of WDR obliquity on Du that further changed with sand size class and moisture state. Finally, the difference in the resulting stress field differentiable by the oblique raindrop trajectories of the experiment over sand surface significantly affected the non-cohesive particle detachment rates, to some extent interacted with size-dependent compressibility and interface shear strength of sand grains. 相似文献
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Tectonometamorphic evolution of the Atbashi high‐P units (Kyrgyz CAOB,Tien Shan): Implications for the closure of the Turkestan Ocean and continental subduction–exhumation of the South Kazakh continental margin 
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下载免费PDF全文 Chloé Loury Yann Rolland Stéphane Guillot Pierre Lanari Clément Ganino Raphael Melis Anthony Jourdon Carole Petit Olivier Beyssac Sylvain Gallet Patrick Monié 《Journal of Metamorphic Geology》2018,36(8):959-985
The South Tien Shan (STS) belt results from the last collision event in the western Central Asian Orogenic Belt (CAOB). Understanding its formation is of prime importance in the general framework of the CAOB. The Atbashi Range preserves high‐P (HP) rocks along the STS suture, but still, its global metamorphic evolution remains poorly constrained. Several HP units have been identified: (a) a HP tectonic mélange including boudins of mafic eclogites in a sedimentary matrix, (b) a large (>100 km long) high‐P metasedimentary unit (HPMU) and (c) a lower blueschist facies accretionary prism. Raman Spectroscopy on carbonaceous material combined with phengite and chlorite multiequilibria and isochemical phase diagram modelling indicates that the HPMU recorded homogeneous P–T conditions of 23–25 kbar and 560–570°C along the whole unit. 40Ar/39Ar dating on phengite from the HPMU ranges between 328 and 319 Ma at regional scale. These ages are interpreted as (re‐) crystallization ages of phengite during Tmax conditions at a pressure range of 20–25 kbar. Thermobarometry on samples from the HP tectonic mélange provides similar metamorphic peak conditions. Thermobarometry on the blueschist to lower greenschist facies accretionary prism indicates that it underwent P–T conditions of 5–6 kbar and 290–340°C, highlighting a 17–20 kbar pressure gap between the HPMU‐tectonic mélange units and the accretionary prism. Comparison with available geochronological data suggests a very short time span between the prograde path (340 Ma), HP metamorphic peak (330 Ma), the Tmax (328–319 Ma) and the final exhumation of the HPMU (303–295 Ma). Extrusion of the HPMU, accommodated by a basal thrust and an upper detachment, was driven by buoyant forces from 70–75 km up to 60 km depth, which directly followed continental subduction and detachment of the HPMU. At crustal depths, extrusion was controlled by collisional tectonics up to shallow levels. Lithological homogeneity of the HPMU and its continental‐derived character from the North Tien Shan suggest this unit corresponds to the hyper‐extended continental margin of the Kazakh continent, subducted southward below the north continental active margin of the Tarim craton. Integration of the available geological data allows us to propose a general geodynamic scenario for Tien Shan during the Carboniferous with a combination of (a) N‐dipping subduction below the Kazakh margin of Middle Tien Shan until 390–340 Ma and (b) S‐dipping subduction of remaining Turkestan marginal basins between 340 and 320 Ma. 相似文献
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Microstructural tectonometamorphic processes and the development of gneissic layering: a mechanism for metamorphic segregation 总被引：6，自引：1，他引：5
The Mary granite, in the East Athabasca mylonite triangle, northern Saskatchewan, provides an example and a model for the development of non-migmatitic gneissic texture. Gneissic compositional layering developed through the simultaneous evolution of three microdomains corresponding to original plagioclase, orthopyroxene and matrix in the igneous rocks. Plagioclase phenocrysts were progressively deformed and recrystallized, first into core and mantle structures, and ultimately into plagioclase-rich layers or ribbons. Garnet preferentially developed in the outer portions of recrystallized mantles, and, with further deformation, produced garnet-rich sub-layers within the plagioclase-rich gneissic domains. Orthopyroxene was replaced by clinopyroxene and garnet (and hornblende if sufficient water was present), which were, in turn, drawn into layers with new garnet growth along the boundaries. The igneous matrix evolved through a number of transient fabric stages involving S-C fabrics, S-C-C' fabrics, and ultramylonitic domains. In addition, quartz veins were emplaced and subsequently deformed into quartz-rich gneissic layers. Moderate to highly strained samples display extreme mineralogical (compositional) segregation, yet most domains can be directly related to the original igneous precursors. The Mary granite was emplaced at approximately 900 °C and 1.0 GPa and was metamorphosed at approximately 750 °C and 1.0 GPa. The igneous rocks crystallized in the medium-pressure granulite field (Opx–Pl) but were metamorphosed on cooling into the high-pressure (Grt–Cpx–Pl) granulite field. The compositional segregation resulted from a dynamic, mutually reinforcing interaction between deformation, metamorphic and igneous processes in the deep crust. The production of gneissic texture by processes such as these may be the inevitable result of isobaric cooling of igneous rocks within a tectonically active deep crust. 相似文献
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Through the use of Jacobi's formulation of the least action principle, differential equations for Szebehely's problem extended to a holonomic system with n degrees of freedom are obtained.
Sunto Si riottengono le equazioni differenziali relative al problema di Szebehely esteso ad un sistema olonomo ad n gradi di libertà utilizzando il principio di minima azione nella formulazione di Jacobi.相似文献