The influence of satellite flexibility on orbital motion     

A. K. Misra  V. J. Modi 《Celestial Mechanics and Dynamical Astronomy》1978,17(2):145-165

The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in =(l/a ₀)²,l anda ₀ being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.List of Symbols A _ij, B_ij coefficients in the eigenfunction expansion ofv _i andw _i respectively, Equation (10) - C _k, D_k constants, Equation (21) - EI _i flexural rigidity of theith appendage - E(u₀) ²(1+e ₀ cosu ₀)² h ₀ ³ - F(u₀) perturbation function, Equation (17b) - F ,F ,F functions of librational angles and flexural displacements, Equation (11i) - F ,F ,F F ,F ,F with change of independent variable fromt tou ₀ - I _xx, I_yy, I_zz principal moments of inertia of the undeformed satellite - [J ⁱ] inertia dyadic of the deformedith appendage - [J _d] inertia dyadic of the deformed satellite - M mass of the satellite - P _R, P_u functions of librational angles and flexural displacements, Equation (15d) and (15e), respectively - R _c magnitude ofR _c - R _c0, R₁ unperturbed value and first order perturbation ofR _c, respectively - R _c ,R ₀ position vectors of the c.m. of the deformed and undeformed satellite, respectively - T kinetic energy of the satellite - U potential energy of the satellite - U _e, U_g elastic and gravitational potential energy, respectively - X, Y, Z orbital co-ordinate axes, located at the c.m. of the deformed satellite - Y ₁(u₀), Y₂(u₀) functions ofu ₀, Equation (18b) and (18c), respectively - a semi-major axis - a ₀ unperturbed value ofa - e eccentricity - e ₀ unperturbed value ofe - h ₀ unperturbed angular momentum per unit mass of the satellite - i inclination of the orbital plane to the ecliptic - i, j, k unit vectors alongx (or ),y (or ) andz (or ) axes, respectively - l characteristic length of the satellite - l _i length of theith appendage - [l ⁱ] matrix of direction cosines ofx _i, v_i andw _i - l ,l ,l direction cosines ofR _c - m ₀, m_i mass of the main body andith appendage, respectively - p _i ² - q _m, Q_m generalized co-ordinate and force, respectively - r ₁ R ₁/R_c0 - r position vector of an element of the body referred toxyz axes - r _u position vector of an element after deformation, referred to axes - r _c x _c i+y _c j+z _c k, position vector of the c.m. of the deformed body referred toxyz axes - s x _i/l_i - t time - u true anomaly - u ₀, u₁ unperturbed value and the first order perturbation ofu, respectively - u elastic displacement vector - u _c u–r _c - velocity of an element relative to axes - v _i, w_i flexural deformations - x, y, z body co-ordinate axes with origin at the c.m. of the undeformed satellite - x _i distance of an element of theith appendage from the root - _j jth eigenfunction (normalized) of a cantilever - angle between the line of nodes and vernal equinox - , , components of nondimensionalized angular velocity of the satellite - , , pitch (spin), yaw and roll, respectively - _i nominal inclination of theith appendage in the orbital plane - - small parameter, (l/a ₀)² - _j jth eigenvalue of a cantilever - gravitational constant - _jk constant, Equation (11j) - , , body co-ordinate axes with origin at the c.m. of the deformed satellite - ( i + j + k), angular velocity of the satellite  相似文献   

Laboratory investigations on rotary diamond drilling     

K. U. M. Rao  A. Bhatnagar  B. Misra 《Geotechnical and Geological Engineering》2002,20(1):1-16

Extensive laboratory drilling investigations were conducted on a wide variety of rocks to study the inter-dependence of machine as well as rock parameters on the performance of the drilling operation. Detailed physical and mechanical properties of all the rock types were determined to study the influence of the rock properties on the drilling performance. The effect of PEO (poly-ethylene-oxide) added to the drilling water was also studied. Slake durability tests were conducted in plain water as well as a PEO mixed water medium to observe the effects of PEO on the surface properties of the rock. An attempt is also made to understand the different modes of wear of impregnated diamond bits in the rotary drilling operation.  相似文献   

Evolution of Mayurbhanj Granite Pluton, eastern Singhbhum, India: a case study of petrogenesis of an A-type granite in bimodal association     

Saumitra Misra  Subha Sankar Sarkar  Sambhunath Ghosh 《Journal of Asian Earth Sciences》2002,20(8)

The A-type Mayurbhanj Granite Pluton (3.09 Ga), occurring along the eastern margin of the Singhbhum-Orissa Craton, eastern India, represents the final phase of acid plutonism in this crustal block of Archean age. The granite shows a bimodal association with a voluminous gabbroid body, exposed mainly along its western margin, and is associated with the Singhbhum Shear zone. The granite pluton is composed mainly of a coarse ferrohastingsite–biotite granite phase, with an early fine-grained granophyric microgranitic phase and a late biotite aplogranitic phase. Petrogenetic models of partial melting, fractional crystallisation and magma mixing have been advocated for the evolution of this pluton. New data, combined with earlier information, suggest that two igneous processes were responsible for the evolution of the Mayurbhanj Granite Pluton: partial melting of the Singhbhum Granite; followed by limited amount of mixing of acid and basic magmas in an anorogenic extensional setting. The necessary heat for partial melting was provided by the voluminous basaltic magma, now represented by the gabbroid body, emplaced at a shallow crustal level and showing a bimodal association with the Mayurbhanj Granite Pluton. The Singhbhum Shear Zone provided a possible channel way for the emplacement of the basic magma during crustal extension. It is concluded that all three phases of the Mayurbhanj Granite Pluton were derived from the same parent magma, generated by batch partial melting of the Singhbhum Granite at relatively high temperatures (980 °C) and low pressures (4 to <2 kbar) under anhydrous conditions. The coarse ferrohastingsite biotite granite phase shows evidence of limited and heterogeneous assimilation of country rock metasediments. However, the early microgranite phase and late aplogranite phase have not assimilated any metasediments. Compositional irregularities observed along the western margin of the Mayurbhanj Granite Pluton in contact with the gabbro body including a continuous fractionating sequence from quartz diorite to alkali-feldspar granite in the Notopahar area. Gradational contacts between the gabbro and the Mayurbhanj Granite Pluton in the Gorumahisani area etc., may be attributed to a limited amount of mixing between the gabbroid magma and the newly generated Mayurbhanj Granite magma. The mixing was mainly of liquid–liquid diffusive type, with a subordinate amount of mixing of solid–liquid type. Although A-type granites are commonly described as having high total REE (e.g. 270–400 ppm), studies on the late aplogranite phase of the Mayurbhanj Granite show that total REE values (100 ppm) are low. This low REE abundance may be attributed to the progressive residual nature of the Singhbhum Granite source during continued partial melting, when the magmas of the microgranite and coarse granite phases had already been removed from the source region.  相似文献   

On thermosolutal-convective instability in a stellar atmosphere     

Sharma  R. C.  Misra  J. N. 《Astrophysics and Space Science》1986,126(2):223-229

Thermosolutal-convective instability of a stellar atmosphere in the presence of a stable solute gradient is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The criteria derived for monotonic instability are found to hold true in the presence of FLR and Hall effects.  相似文献   

Escalation of salinity levels in the quaternary aquifers of the Ganga alluvial plain,India     

Anil Kumar Misra  Ajai Mishra 《Environmental Geology》2007,53(1):47-56

A detailed water quality analysis was carried out in the quaternary aquifer system of the marginal alluvial plain (Ganga Plain) in Bah Tahsil, Agra district, India. The electrical conductivity of 50 samples each from dug wells, hand pumps and tube wells was analysed for the study of salinity levels in shallow, intermediate and deep aquifers. Out of 50, 20 samples of each were also analysed for other chemical constituents such as Na⁺, K⁺, Cl⁻, F⁻ and TDS. The analyses show drastic changes in the salinity levels of shallow, intermediate and deep aquifers. The deep aquifers are more saline compared to the shallow and intermediate aquifers. On the contrary, the concentration of chemical constituents such as Na⁺, K⁺, Cl⁻ and F⁻ was more in the shallow aquifers compared to the deep aquifers. Moreover, there is an indication that the salinity and concentration of the above chemical constituents also escalate with time in each aquifer. The chemical constituents such as Na⁺, K⁺, Cl⁻, F⁻ and TDS range from 51 to 165 mg/l, 1 to 14 mg/l, 224 to 1,459 mg/l, 0 to 1.5 mg/l and 750 to 2,650 mg/l, respectively. Over a 3-year period, the salinity levels have sharply increased and the average F level has increased by 0.1–0.3 mg/l. An attempt has been made here to discuss the factors causing the variation and escalation of chemical constituents and salinity in the water of the three aquifers.  相似文献   

Whistler Mode Instability in a Lorentzian (κ) Magnetoplasma in the Presence of Perpendicular A.C. Electric Field and Cold Plasma Injection     

Tripathi  A. K.  Misra  K. D. 《Earth, Moon, and Planets》2000,88(3):131-153

The dielectric tensor, modified plasma dispersion function and dispersion relation for Whistler mode instability in an infinite magnetoplasma are obtained in the case of cold plasma injection to background hot anisotropic generalized bi-Lorentzian (κ) plasma in the presence of external perpendicular a.c. electric field. The method of characteristics solutions using perturbed and unperturbed particle trajectories have been used to determine the perturbed distribution function. Integrals and modified plasma dispersion function Z_κ ^*(ξ ) are reduced in power series expansion form. Numerical methods using computer technique have been used to obtained temporal growth rate for magnetospheric plasma at geostationary height. The bi-Lorentzian (κ) plasma is reducible to various forms of distribution function by changing the spectral index κ. The results of bi-Lorentzian (κ) plasma are compared with those of bi-Maxwellian plasma. It has been found that the addition of cold plasma injection gives different frequency spectra. The a.c. frequency of moderate amplitude increases the growth rate and instability in K space to lower range. Growth rate maximum is not affected by a.c. frequencies. However, it shifts the maximum to lower K space in both cases, rather than on the variation of the magnitude. Thus a physical situation like this may explain emission of various high frequency whistler emissions by cold plasma injection. The potential application of controlled plasma experiments in the laboratory and for planetary atmosphere are indicated. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

A quantum chemical study on the formation of ethanimine (CH<Subscript>3</Subscript>CHNH) in the interstellar ice     

Keshav Kumar Singh  Shivani  Poonam Tandan  Alka Misra 《Astrophysics and Space Science》2018,363(10):213

Ethanimine (CH₃CHNH) is an important prebiotic molecule since it is a precursor of amino acid \(\alpha \)-alanine in Strecker synthesis. Two isomers (E and Z) of ethanimine were detected in the molecular cloud Sagittarius B2 north during GBT-PRIMOS survey. A possible radical-molecule reaction pathway has been proposed for the formation of ethanimine in the interstellar medium (ISM) from some previously detected interstellar molecules like methylene (both triplet CH₂ (³B₁) and singlet CH₂ (¹A₁)) and methyenimine (CH₂NH). The mechanism has been studied in the gas phase and in water ice with the help of density functional theory at B2PLYPD/6-311++G (2d, p) level of theory. It is observed that E-ethanimine forms efficiently in gas phase but ice reactions are favorable only in the hot core of molecular clouds. Same is true for the formation of Z-ethanimine which forms only at the surface of water cluster as the height of entrance barrier for formation of Z-ethanimine is similar to that of E-ethanimine. Isomerization from E to Z form is also studied and found to be forbidden due to large entrance barrier. Out of the two reaction system CH₂ (³B₁) + CH₂NH and CH₂ (¹A₁) + CH₂NH, later is more favorable then the former one due to the small entrance barrier. Still, much of the detected abundance of ethanimine comes from the reaction of CH₂ (³B₁) with CH₂NH as since CH₂ (¹A₁) has very low abundance compared to the CH₂ (³B₁) in ISM. The proposed pathway seems to be a promising candidate for the ethanimine formation in ISM.  相似文献   

Systematic analysis of low/hard state RXTE spectra of GX 339–4 to constrain the geometry of the system     

Kalyani Bagri  Ranjeev Misra  Anjali Rao  Jagdish Singh Yadav  Shiv Kumar Pandey 《天文和天体物理学研究(英文版)》2018,(5)

One of the popular models for the low/hard state of black hole binaries is that the standard accretion disk is truncated and the hot inner region produces, via Comptonization, hard X-ray flux.This is supported by the value of the high energy photon index, which is often found to be small,～ 1.7( 2), implying that the hot medium is starved of seed photons. On the other hand, the suggestive presence of a broad relativistic Fe line during the hard state would suggest that the accretion disk is not truncated but extends all the way to the innermost stable circular orbit. In such a case, it is a puzzle why the hot medium would remain photon starved. The broad Fe line should be accompanied by a broad smeared reflection hump at ～ 30 ke V and it may be that this additional component makes the spectrum hard and the intrinsic photon index is larger, i.e. 2. This would mean that the medium is not photon deficient, reconciling the presence of a broad Fe line in the observed hard state. To test this hypothesis,we have analyzed the RXTE observations of GX 339–4 from the four outbursts during 2002–2011 and identify observations when the system was in the hard state and showed a broad Fe line. We have then attempted to fit these observations with models, which include smeared reflection, to understand whether the intrinsic photon index can indeed be large. We find that, while for some observations the inclusion of reflection does increase the photon index, there are hard state observations with a broad Fe line that have photon indices less than 2.  相似文献   

The seasonal predictability of the Asian summer monsoon in a two-tiered forecast system     

Vasubandhu Misra  H. Li 《Climate Dynamics》2014,42(9-10):2491-2507

An extensive set of boreal summer seasonal hindcasts from a two tier system is compared with corresponding seasonal hindcasts from two other coupled ocean–atmosphere models for their seasonal prediction skill (for precipitation and surface temperature) of the Asian summer monsoon. The unique aspect of the two-tier system is that it is at relatively high resolution and the SST forcing is uniquely bias corrected from the multi-model averaged forecasted SST from the two coupled ocean–atmosphere models. Our analysis reveals: (a) The two-tier forecast system has seasonal prediction skill for precipitation that is comparable (over the Southeast Asian monsoon) or even higher (over the South Asian monsoon) than the coupled ocean–atmosphere. For seasonal anomalies of the surface temperature the results are more comparable across models, with all of them showing higher skill than that for precipitation. (b) Despite the improvement from the uncoupled AGCM all models in this study display a deterministic skill for seasonal precipitation anomalies over the Asian summer monsoon region to be weak. But there is useful probabilistic skill for tercile anomalies of precipitation and surface temperature that could be harvested from both the coupled and the uncoupled climate models. (c) Seasonal predictability of the South Asian summer monsoon (rainfall and temperature) does seem to stem from the remote ENSO forcing especially over the Indian monsoon region and the relatively weaker seasonal predictability in the Southeast Asian summer monsoon could be related to the comparatively weaker teleconnection with ENSO. The uncoupled AGCM with the bias corrected SST is able to leverage this teleconnection for improved seasonal prediction skill of the South Asian monsoon relative to the coupled models which display large systematic errors of the tropical SST’s.  相似文献   

Modeling the depletion of dissolved oxygen in a lake due to algal bloom: Effect of time delay     

A.K. Misra  Peeyush ChandraV. Raghavendra 《Advances in water resources》2011,34(10):1232-1238

We propose and analyze a non-linear mathematical model for algal bloom in a lake to account for the delay in conversion of detritus into nutrients. It is assumed that there is a continuous inflow of nutrients in the lake due to agricultural run off. The model involves four variables, namely nutrient concentration, algal population density, detritus density and dissolved oxygen concentration. The dynamics of the model is studied in terms of local stability analysis and Hopf-bifurcation analysis. It is found that the positive equilibrium of the model may switch from stability to instability to stability, and eventually instability sets in under certain conditions. The numerical simulation is performed to support the analytical results.  相似文献