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1.
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
2.
Cristina Stoica 《Celestial Mechanics and Dynamical Astronomy》2002,84(3):223-229
The present paper offers an alternative point of view of block regularization for the motion of a particle in a central potential field of the form –x
–, where x is the distance between the particle and the source and some positive real number.Working in the physical space, we consider the scattering angle determined by the path of the particle as a function of angular momentum. We prove that a particle flow is passing over the collision singularity preserving differentiability with respect to initial data if and only if = 2(1–1/n), n positive integer, n 2.This result coincides with the outcome of block regularization applied by McGehee to the same dynamical problem. We discuss that this identity was to expect since both methods target the same physical constraint over the flow. 相似文献
3.
4.
Dean F. Smith 《Solar physics》1972,23(1):191-203
The processes by which streams of charged particles become charge and current neutralized in the corona are investigated. It is shown that a large amplitude plasma wave, which is related to precursor phenomenon in type III bursts and possibly plasma radiation from type IV bursts, will be excited at the head of the stream. The energy extracted from the stream to produce this plasma wave is computed and used to set conservative upper limits on the densities of possible excitors for type III bursts. For electron streams the density n
s < 10–5
n
e, where n
e is the density of the background plasma. For proton streams n
s < 1.8 × 10–2
n
e. The energy extracted from the stream is also used to set upper limits on the lifetimes of relativistic electrons stored in the corona and it is concluded that for n
e > 102 cm–3 this loss must be taken into account. Since electron streams cannot produce their own stabilizing ionacoustic waves because they would violate the condition n
s < 10–5
n
e, other mechanisms for producing ion-acoustic waves in the corona are examined. Another stabilization mechanism due to velocity inhomogeneity is investigated.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
5.
High‐resolution mass spectrometry (HRMS) imaging by desorption electrospray ionization (DESI) coupled with Orbitrap MS using methanol (MeOH) spray was performed on a fragment of the Murchison (CM2) meteorite in this study. Homologues of CnH2n–1N2+ (n = 7–9) and CnH2nNO+ (n = 9–14) were detected on the sample surface by the imaging. A high‐performance liquid chromatography (HPLC)/HRMS analysis of MeOH extracts from the sample surface after DESI/HRMS imaging indicated that the CnH2n–1N2+ homologues corresponds to alkylimidazole, and that a few isomers of the CnH2nNO+ homologues present in the sample. The alkylimidazoles and CnH2nNO+ homologues displayed different spatial distributions on the surface of the Murchison fragment, indicating chromatographic separation effects during aqueous alteration. Moreover, the distribution pattern of compounds is also different among homologues. This is probably also resulting from the separation of isomers by similar chromatographic effects, or different synthetic pathways. Alkylimidazoles and the CnH2nNO+ homologues are mainly distributed in the matrix region of the Murchison by mineralogical observations, which is consistent with previous reports. Altered minerals (e.g., Fe‐oxide, Fe‐sulfide, and carbonates) occurred in this region. However, no clear relationship was found between these minerals and the organic compounds detected by DESI/HRMS imaging. Although this result might be due to scale differences between the spatial resolution of DESI/HRMS imaging and the grain size in the matrix of the Murchison, our results would indicate that alkylimidazoles and the CnH2nNO+ homologues in the Murchison fragment were mainly synthesized by different processes from hydrothermal alteration on the parent body. 相似文献
6.
Yoshihide Kozai 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):365-370
In this paper dynamical characteristics of satellites are outlined by classifying the satellites into three categories according to the values of the solar tidal factor (n/n)2 which is the disturbing factor due to the sun and the oblateness factor of the primary planetJ
2/a
2. For inner satellites (n/n)2 is much smaller thanJ
2/a
2 and there are several pairs among them, for which the mean motions are commensurable to each other, and for some of them secular accelerations in the mean longitudes have been detected. For outer satellites (n/n)2 is much larger and the solar perturbations are dominant. For intermediary satellites the motion of the pole of the orbital plane is not so simple as those of the satellites of the other categories. 相似文献
7.
In the present article, a family of static spherical symmetric well behaved interior solutions is derived by considering the
metric potential g
44=B(1−Cr
2)−n
for the various values of n, such that (1+n)/(1−n) is positive integer. The solutions so obtained are utilised to construct the heavenly bodies’ like quasi-black holes such
as white dwarfs, neutron stars, quarks etc., by taking the surface density 2×1014 gm/cm3. The red shifts at the centre and on the surface are also computed for the different star models. Moreover the adiabatic
index is calculated in each case. In this process the authors come across the quarks star only. Least and maximum mass are
fond to be 3.4348M
Θ and 4.410454M
Θ along with the radii 21.0932 km and 23.7245 km respectively. 相似文献
8.
Atomic self consistent field calculations are applied to identify Fe VI and Fe VII spectra belonging to the 3p
6 3d
n — 3p
5 3d
n + 1 transition arrays. Their presence in vacuum spark spectra and absence in solar spectrograms is discussed. 相似文献
9.
Yong Gwan Yi 《Astrophysics and Space Science》2011,336(2):347-355
An optical approach begins by interpreting the gravitational redshift resulting to a change in the relative velocity of light
due to the medium of propagation in the gravitational field. The discussion continues by pointing out an agreement in structure
between the equation for rays in geometrical optics and the geodesic equation of general relativity. From their comparison
we learn that the path of rays should be written in the form ds
2=n
2(r)dr
2+r
2
dθ
2, not ds
2=dr
2+r
2
dθ
2, in a medium with spherical symmetry of refractive index n(r). The development of an optical analogy suggests introducing n
2(r) in place of g
rr
as an optical version of the Schwarzschild metric. In form and content, n
2(r) is different from g
rr
. The optical point of view replaces the general-relativity explanations in terms of time and gravitation. 相似文献
10.
The gravitational instability of a nonrotating isothermal gaseous disk permeated by a uniform frozen-in magnetic field is investigated using a fourth-order perturbation technique. From the results it is found that the disk is stable whenn/B
0 < (4/33
G)–1/2, wheren andB are the column density of the disk and unperturbed magnetic field, respectively, andG is the gravitational constant. The disk is gravitationally unstable only whenn/B
0 > (4/33
G)–1/2. 相似文献
11.
Nevena Markova 《Astrophysics and Space Science》1989,158(1):89-93
Sixty-two spectrograms of the supergiant P Cyg, obtained with the Coudé spectrograph of the 2 m RCC telescope at NAO (National Astronomical Observatory, Bulgaria) were used in order to study the behaviour (we mean the displacements of the absorption components only) of the Hei spectrum of this star. Twelve lines from four series (23
P
0–n3S, 23P0
–n
3
D, 2
1
P
0
–n
1
D, and 21
S–n
1
P
0) were examined. It was established that all observed cases can be reduced to a few (three or four) which are typical. These cases are stated in the form of the comparison between the hydrogen and helium lines. All profiles were rectified and their complex structure was taken into consideration. The fixed peculiarities were explained by an optical depth effect. 相似文献
12.
In this paper, we have investigated that tilted Bianchi Type I cosmological models for stiff perfect fluid under a supplementary
condition A = B
n
between metric potentials, is not possible. The tilted solution is also not possible when we assume A = t
ℓ, B = t
m
, C = t
n
; ℓ, m and n are constants for ε = p. Thus to preserve tilted nature of model, we assume p = γε, 0 ≤ γ ≤ 1 (barotropic equation of state) for the case A = t
ℓ
B = t
m
and C = t
n
. The physical and geometrical aspects of the models are also discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric
metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g
44=B(1+Cr
2)
n
, where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing
with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained
at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar
mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already
known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved. 相似文献
14.
This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely
n
=
o
(n + 1)1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency
n
= (
n
2
+
H
2
)1/2 should be found in observational data. 相似文献
15.
Kuniaki Masai 《Astrophysics and Space Science》1984,106(2):391-407
The effect of X-ray irradiation on the line-driven stellar wind in X-ray binary systems is studied. The product of the X-ray luminosityL
x and the densityn in the wind is a measure to distinguish between the optically thin and thick wind regimes. For an X-ray source of the radiation temperature of 10 keV, the critical value(L
x
n)
c
, is of the order of 1037 erg s–1 cm–3; hence, most of wind-fed X-ray sources lie in the optically thick wind regime because ofL
x
n>(L
x
n)
c
. Then the wind structure is determined not only by the parameter =(L
x
/nR
2),R the distance from the X-ray source, but also by the optical thickness due to helium. The formation of fully ionized helium region depends onL
x
andn in a way different from that of the Strömgren sphere. In such an optically thick wind, the region behind the He II ionization boundary is little affected by X-ray irradiation and the trace elements remain to be responsible for wind acceleration. Thus, its location is important for the structure of the wind and the interpretation of various phenomena in objects such as wind-fed X-ray pulsars. 相似文献
16.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1979,63(2):295-317
General integral transform of the exponential integralsE
n
is considered and will be denoted asB
(k)
n
(). Different expressions and the equations satisfied byB
(k)
n
are developed. Two-term recurrence formula forB
(k)
n
(0) and three-term recurrence formula forB
(k)
n
(); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy 相似文献
17.
Arnold Stokes 《Celestial Mechanics and Dynamical Astronomy》1978,17(2):137-144
When integrating a perturbed two-body problem, very often the propagation of the numerical error is reduced by using a new time variables defined by dt/ds=|q|
n
, (|q| is the radial distance,t the time). This paper introduces a time element for such transformations, i.e., a new variablet
n is defined so that dt
n/ds=1+ (perturbing terms) andt=F
n(tn), whereF
n is a known function. The time element equation should be useful in reducing the error in the determination of the timet.F
n is given explicitly forn=1, 3/2, 2, 5/2 and 3, and a general expression is given for other values.The work was performed while the author was an NRC Senior Research Associate, Goddard Space Flight Center, Greenbelt, Md., U.S.A. 相似文献
18.
Populations of Rydberg levels of atoms are calculated including effects of lowering the atomic ionization potential. Due to these effects the boundary conditions in bn problem is lim bn = 0. The bn factors were computed for T = 100 K. Ne = 0.1 cm−3 with bn = 0 when n ≧ 3000. The result allows to interpret observational data of the carbon decametric lines without the use of the subthermal dielectronic recombination mechanism. The calculations predict high relative intensities of Cnβ and Cnγ lines. 相似文献
19.
Jaume Llibre 《Celestial Mechanics and Dynamical Astronomy》1990,50(1):89-96
Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m
1,..., m
n we denote by N(m
1, ..., m
n, k) the number of central configurations' of the n-body problem in k modulus dilatations and rotations. If m
n
1,..., m
n, k) is finite, then we give a bound of N(m
1,..., m
n, k) which only depends of n and k. 相似文献
20.
Andrzej J. Maciejewski Maria Przybylska 《Celestial Mechanics and Dynamical Astronomy》2004,89(2):145-164
We consider two fixed centres attracting a third body. Each centre is the source of a force field with potential V=−ar
−2n
, where n is a real number. We prove that this generalization of the classical two fixed centres problem is non-integrable except when
n= 0, 1/2, −1 and −2.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献