共查询到20条相似文献，搜索用时 625 毫秒
1.
R. A. Howland 《Celestial Mechanics and Dynamical Astronomy》1988,44(3):209-226
The librational motion of the Ideal Resonance Problem (Garfinkel, 1966, Jupp, 1969) is treated through an initialnon-canonical transformation which, however, leaves the equations of motion in a quasi-canonical form, with Hamiltonian expressed in standard trigonometric functions amenable to traditional averaging techniques. The perturbed solutions, similarly expressed intrigonometric near-identity transformations, and their frequencies can be found to arbitrary order, with the elliptic integrals expected of the system introduced only in a final explicit quadrature for a Kepler-type equation in the angular variable. The specific transformations and resulting equations of motion are introduced, and explicit solutions for the original variables are found to second order, with mean motion accurate to fifth. Limitation of the present solution to the librational region, the extension of that solution to higher order, and observations on the form of the associated Hamiltonian are also discussed. 相似文献
2.
The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a Kepler-equation. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians. 相似文献
3.
John E. Cochran 《Celestial Mechanics and Dynamical Astronomy》1972,6(2):127-150
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/0, wheren is the orbital mean motion of the center of mass and0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made. 相似文献
4.
Sandro da Silva Fernandes 《Celestial Mechanics and Dynamical Astronomy》1995,63(3-4):375-408
Expansions of the functions (r/a)cos
jv and (r/a)m
sin
jv of the elliptic motion are extended to highly eccentric orbits, 0.6627 ... <e<1. The new expansions are developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of these expansions are expressed in terms of the derivatives of Hansen's coefficients with respect to the eccentricity. The new expansions are convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is the same of the extended solution of Kepler's equation. The new expansions are intrinsically related to Lagrange's series. 相似文献
5.
C. Marchal 《Celestial Mechanics and Dynamical Astronomy》1986,38(4):377-387
With the Hamiltonian parameters developed for the two-fixed-centers problem a simple and very accurate expression of the quasi-integral can be given for the motion of artificial satellites perturbed by the Earth's zonal harmonics. This motion can be considered as integrable.A theoretical analysis shows that Hénon's semi-ergodic regions or chaotic regions are extremely small in this problem, and almost all orbits are of the regular or quasi-periodic type. Furthermore, the relative difference between the true motion and the corresponding integrable motion remains forever less than 10–14 for all regular orbits even in the vicinity of critical inclinations.For chaotic orbits this very small difference remains verified at least for centuries, nevertheless there are some exceptional orbits that finally diverge from the integrable model. 相似文献
6.
Alan H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1974,8(4):523-530
In an earlier publication (Jupp, 1972), a solution of the Ideal Resonance Problem is exhibited explicitly in terms of the mean elements; to second order in the small parameter in the case of libration, and to first order in the case of deep circulation. Both representations possess a singularity when the mean modulus of the Jacobi elliptic functions is unity; this corresponds to the separatrix of the phase plane of the dynamical system.It is shown here that, provided particular coefficients associated with the problem satisfy specific relations, the singularity is removed, and the resulting solution is applicable throughout the deep resonance region.The solution is then expressed in terms of general initial conditions. Again, in general, the solution has a singularity associated closely with the limiting motion, and the circulation part of the solution is restricted to deep circulation. It is shown that when the previously-mentioned coefficients satisfy particular constraints, the singularity is removed. In addition, with the same constraints, the deep-circulation solution is applicable throughout the circulation region. It is of interest that these constraints are quite different from those associated with the mean, element formulation. 相似文献
7.
N. F. Martinova 《Celestial Mechanics and Dynamical Astronomy》1976,13(3):363-381
This paper deals with a three-dimensional rotationally and dynamically symmetrical satellite. The centre of mass of the satellite moves in a circular orbit. The existence of two first integrals of motion enables one to transform the system of differential equations to a special form facilitating the choice of the zero-approximation solution. The angles of precession and nutation as well as the amplitude functionk
2(t) are taken as variables of the motion. The first approximation solution is constructed for the case of spatial libration of the satellite axis of dynamical symmetry about the position of stable equilibrium. The series representing the functionk
2(t) is fast convergent due to the fast convergence of the expansions for elliptic functions. 相似文献
8.
K. Zare 《Celestial Mechanics and Dynamical Astronomy》1982,26(4):407-412
The time transformation dt/ds=r
is studied in detail and numerically stablized differential equations are obtained for =1,2, and 3/2. The case =1 corresponds to Baumgarte's results. 相似文献
9.
Efi Meletlidou Simos Ichtiaroglou Fabian Josef Winterberg 《Celestial Mechanics and Dynamical Astronomy》2001,80(2):145-156
We prove that Hill's lunar problem does not possess a second analytic integral of motion, independent of the Hamiltonian. In order to obtain this result, we avoid the usual normalization in which the angular velocity of the rotating reference frame is put equal to unit. We construct an artificial Hamiltonian that includes an arbitrary parameter b and show that this Hamiltonian does not possess an analytic integral of motion for in an open interval around zero. Then, by selecting suitable values of , b and using the invariance of the Hamiltonian under scaling in the units of length and time, we show that the Hamiltonian of Hill's problem does not possess an integral of motion, analytically continued from the integrable two–body problem in a rotating frame. 相似文献
10.
Jack Wisdom 《Celestial Mechanics and Dynamical Astronomy》1986,38(2):175-180
The solution by Sessin and Ferraz-Mello (Celes. Mech.
32, 307–332) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 21 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem. 相似文献
11.
In the present paper, the effects of free convection currents and the viscous dissipation on the unsteady flow of an electrically conducting and viscous incompressible fluid around an uniformly accelerated vertical porous plate subjected to a suction or injection velocity inversely proportional to the square root of time, in presence of a transverse magnetic field, have been investigated. Analytical solutions for the velocity and the temperature distributions, the skin-friction and the rate of heat transfer are obtained for small magnetic parameterM. During the course of discussion the effects of the Grashof number Gr, the Eckert number Ec, the suction/injection parametera have been considered for unit value of the Prandtl number Pr.Nomenclature
a
suction/injection parameter
-
C
p
specific heat at constant pressure
-
B
0
magnetic induction
-
g
acceleration due to gravity
- Gr
Grashof number (g(T
w
–T
)/U
0
3
)
-
K
thermal conductivity
-
M
magnetic field parameter (B
0
2
/U
0
2
)
- Pr
Prandtl number (C
p/K)
-
T
temperature of the fluid near the plate
-
T
w
temperature of the plate
-
T
temperature of the fluid at infinity
-
t
time
-
t
dimensionless time (tU
0
2
/)
-
u
velocity of the fluid
-
u
non-dimensional velocity (u/U
0)
-
U
velocity of the plate
-
U
dimensionless velocity of the plate (U/U
0)
-
U
0
reference velocity
-
v
0
suction velocity
-
v
0
non-dimensional suction velocity (v
0/U
0)=at
–1/2
- Ec
Eckert number ((U
0)2/3/C
p(T
w
–T
))
-
T
dimensionless temperature of the fluid near the plate ((T–T
)/(T
w
–T
))
-
x, y
coordinates along and normal to the plate
-
x, y
dimensionless coordinates (y=yU
0/)
-
kinematic viscosity
-
coefficient of volume expansion
-
electric conductivity of the fluid
-
y/2t
1/2
-
density of the fluid
-
skin-friction
-
dimensionless skin-friction
-
q
rate of heat transfer
-
q
non-dimensional rate of heat transfer
-
coefficient of viscosity
- e
magnetic permeability
On leave of absence from Department of Mathematics, University of Dhaka, Bangladesh 相似文献
12.
Walter Petry 《Astrophysics and Space Science》1986,124(1):63-82
We start from a reference frame for which the pseudo-Euclidean geometry holds, i.e., all laws in have the form of special relativity. The geometry of a reference frame , moving with constant velocity with regard to , is received by using the well-known Galilei-transformation for the covariant space-time vector. In the geometry is different from the pseudo-Euclidean one, i.e., the principle of special relativity does not hold. The velocity of light in is direction dependent but the null result of the Michelson-Morley experiment is received. Several useful transformation formulae are given. In particular, we obtain the Marinov-transformation as transformation from the frame to , and conversely. Maxwell's equations and the equations of motion in the reference frame are given. The theory is applied to some examples, e.g., the Doppler effect, the Fizeau experiment, the field of a charged particle, etc. The method can be generalized to an accelerated reference frame . 相似文献
13.
I. Lerche 《Astrophysics and Space Science》1978,53(1):21-37
We investigate the one-dimensional self-similar flow behind a blast wave from a plane explosion in a medium whose density varies with distance asx
– with the assumption that the flow is isothermal. If <0 a continuous solution passing through the origin and the shock does not exist. If 1/3>>0 one critical point exists. To be physically acceptable the flow must by-pass this critical point. It is shown that a continuous solution passing through both the origin and through the shock and by-passing the critical point does exist. If 1>>1/3 the first critical point does not exist but a second one appears. To be physically acceptable the flow must again by-pass this new critical point. We show that a continuous solution passing through both the origin and the shock and by-passing the new critical point exists in this case. If >1 no physically acceptable solution exists since the mass behind the shock is infinite.The dependence of the solutions on the parameter is analytic for >0 so that interpolation between neighboring values of is permitted.We investigate the stability of these isothermal blast waves to one-dimensional but non-self-similar perturbations. If 0<<5/7, the solutions are shown to be linearly unstable against short wavelength perturbations near the origin. If the solution crosses the shock with a normalized velocityu>2 the solution is linearly unstable against short wavelength perturbations near the shock for 1>>0. If the solution crosses the shock with normalized velocity 2>u>1 (and it must cross the shock withu>1), the solution is certainly unstable against short wavelength perturbations near the shock for >11/19 and, depending on the crossing velocity, can be unstable there for all .Thus for 1>>0, the solution is always unstable somewhere. Since there is no characteristic time scale in the system all instabilities grow as a power law of time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form. 相似文献
14.
In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory, i.e. series expansions in the small parameter . For any order of normalization, we give a lower bound
*
r
for the convergence radius of the normalized Hamiltonian, and a greater bound for the remainder, i.e. the non normalized part of the Hamiltonian. As an application, we consider the case of weakly coupled harmonic oscillators with highly nonresonant frequencies and show how, by optimizing, for fixed , the orderr of normalization, one gets for the remainder a greater bound of the formAe
–(*1/)
a
, with positive constantsA,a and
1
*
exponential estimate of Nekhoroshev's type. 相似文献
15.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1980,22(1):19-23
A review is given of the determination of the long-term motion of Pluto. In particular, the discovery of the librational character of the two critical arguments is discussed. The stability of the motion of Pluto is shown to have been established when allknown gravitational forces are considered.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978. 相似文献
16.
Robert L. Oldershaw 《Astrophysics and Space Science》1986,128(2):449-453
The conceptual foundations of the Self-Similar Cosmology and recent successful tests of its scale transformation equations are briefly reviewed. The fact that even physical constants must partake in proper scale transformations suggests a particularly simple, though necessarily speculative, rationale for the observed cosmological self-similarity. This explanation involves the introduction of a Strong Principle of Self-Similarity and a Principle of Scale Covariance. 相似文献
17.
J. Seimenis 《Astrophysics and Space Science》1990,170(1-2):205-208
We develop a new method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. The idea of the method is to express the solution of the nonlinear ODE in the formx=N/D
n
, whereN andD are Fourier series andn is an appropriate constant. We apply this method to a galactic potential with three degrees of freedom.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain. 相似文献
18.
J. S. Watson G. D. Mistretta N. L. Bonavito 《Celestial Mechanics and Dynamical Astronomy》1975,11(2):145-177
In order to retain separability in the Vinti theory of Earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all, altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program.Results of this technique for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by this theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time. 相似文献
19.
Joachim Baumgarte Wolfgang von Grünhagen 《Celestial Mechanics and Dynamical Astronomy》1979,20(2):173-178
This paper shows that for the free symmetric top a formulation of the equations of motion is possible, which is Liapunov stable. The formalism applied is equivalent to the conservative stabilization of the Keplerian problem. The perturbed problem appears in -stable form. This stabilization procedure could be useful in celestial mechanics, if the gyroscopic motion of a satellite is considered and one is interested in the exact position of the angles. 相似文献
20.
The behaviour of the primary and secondary components in a sample of double-lined Algol-type eclipsing binaries in the logg-logT
e diagram is analyzed. Our results indicate that the hotter components behave like normal Main-Sequence stars while the effect of irradiation may partly explain the overluminosity of the cool components.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain. 相似文献