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## Stability of resonant planetary orbits in binary stars

### Journal of Astrophysics and Astronomy (1989-12-01) 10: 347-365 , December 01, 1989

This paper contains a numerical study of the stability of resonant orbits in a planetary system consisting of two planets, moving under the gravitational attraction of a binary star. Its results are expected to provide us with useful information about real planetary systems and, at the same time, about periodic motions in the general four-body problem (G4) because the above system is a special case of G4 where two bodies have much larger masses than the masses of the other two (planets). The numerical results show that the main mechanism which generates instability is the destruction of the Jacobi integrals of the massless planets when their masses become nonzero and that resonances in the motion of planets do not imply, in general, instability. Considerable intervals of stable resonant orbits have been found. The above quantitative results are in agreement with the existing qualitative predictions

## Structure and stability of rotating fluid disks around massive objects. I. Newtonian formulation

### Journal of Astrophysics and Astronomy (1981-12-01) 2: 421-437 , December 01, 1981

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ*=* 5/3 the disk is stable with frequency (MG/r^{3})^{1/2} for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_{c} for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations.

## The Newtonian forces in the Kerr geometry

### Journal of Astrophysics and Astronomy (1990-03-01) 11: 29-35 , March 01, 1990

We study the properties of the ’Newtonian forces’ acting on a test particle in the field of the Kerr black hole geometry. We show that the centrifugal force and the Coriolis force reverse signs at several different locations. We point out the possible relevance of such reversals particularly in the study of the stability properties of the compact rotating stars and the accretion discs in hydrostatic equilibria

## Nonlinear Schrödinger equation for optical media with quintic nonlinearity

### Pramana (1996-04-01) 46: 305-314 , April 01, 1996

A nonlinear quintic Schrödinger equation (NLQSE) is developed and studied in detail. It is found that the NLQSE has soliton solutions, the stability of which is analysed using variational method. It is also found that the soliton pulse width in the materials supporting NLQSE is small compared to soliton pulse width of the commonly studied nonlinear cubic Schrödinger equation (NLCSE).

## Genericity and stability of naked singularities arising in an inhomogeneous dust collapse

### Pramana (1999-08-01) 53: 253-269 , August 01, 1999

In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate *r*. We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense.

## Comparing maps to symplectic integrators in a galactic type Hamiltonian

### Journal of Astrophysics and Astronomy (2003-09-01) 24: 85-97 , September 01, 2003

We obtain the*x - p*_{x}Poincare phase plane for a two dimensional, resonant, galactic type Hamiltonian using conventional numerical integration, a second order symplectic integrator and a map based on the averaged Hamiltonian. It is found that all three methods give good results, for small values of the perturbation parameter, while the symplectic integrator does a better job than the mapping, for large perturbations. The dynamical spectra are used to distinguish between regular and chaotic motion.

## Effect of phase fluctuation on a system of rotating superfluid

### Pramana (1988-03-01) 30: L255-L257 , March 01, 1988

It has been shown that when the root-mean-square of the gradient of phase fluctuation exceeds the inverse of the coherence length a system of superfluid rotating with angular velocity exceeding the critical angular velocity has an instability.

## Periodic orbits in three-dimensional planetary systems

### Journal of Astrophysics and Astronomy (1989-12-01) 10: 367-380 , December 01, 1989

Three-dimensional planetary systems are studied, using the model of the restricted three-body problem for Μ =.001. Families of three-dimensional periodic orbits of relatively low multiplicity are numerically computed at the resonances 3/1, 5/3, 3/5 and 1/3 and their stability is determined. The three-dimensional orbits are found by continuation to the third dimension of the vertical critical orbits of the corresponding planar problem

## Structure and stability of rotating fluid disks around massive objects. II. General relativistic formulation

### Journal of Astrophysics and Astronomy (1982-06-01) 3: 193-206 , June 01, 1982

In this paper we have considered the structure of a thick perfect fluid disk of constant density rotating around a Schwarzschild black hole and its stability under axisymmetric perturbation. The inner edge of such disk cannot lie within 4m. The critical γ_{c} for neutral stability is found to be much less than 4/3 indicating that the disks are generally stable

## On the effect of the eccentricity of a planetary orbit on the stability of satellite orbits

### Journal of Astrophysics and Astronomy (1990-03-01) 11: 11-22 , March 01, 1990

The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic orbits, bifurcating from the Lagrangian points L_{1}, L_{2} of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these exponents are positive, indicating the existence of chaotic motions