相关论文: On the Jacobi-Metric Stability Criterion

The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our…

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…

The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…

The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the…

Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…

This paper introduces an innovative method for ensuring global stability in a broad array of nonlinear systems. The novel approach enhances the traditional analysis based on Jacobian matrices by incorporating the Taylor series boundary…

The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of…

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity. Following previous studies in the literature, we introduce an explicit…

For algebro-geometric study of J-stability, a variant of K-stability, we prove a decomposition formula of non-archimedean $\mathcal{J}$-energy of $n$-dimensional varieties into $n$-dimensional intersection numbers rather than…

We consider the tidal forces between test particles falling along geodesics in the exterior spacetime generated by a static and axially symmetric compact matter source with non-vanishing mass quadrupole. Specifically, we analyze the radial…

We complete the stability study of general relativistic spherically symmetric polytropic perfect fluid spheres, concentrating attention to the newly discovered polytropes containing region of trapped null geodesics. We compare the methods…

We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula…

We investigate the curvature-dependence of the visco-elastic Taylor-Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined.…

Here, we address a uniqueness structure of viscosity solutions for ergodic problems of weakly coupled Hamilton-Jacobi systems. In particular, we study comparison principle with respect to generalized Mather measures as a generalization of…

This paper introduces an algorithmic approach to the analysis of Jacobi stability of systems of second order ordinary differential equations (ODEs) via the Kosambi--Cartan--Chern (KCC) theory. We develop an efficient symbolic program using…

We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…

Jacobi's action principle is known to lead to a problem of time. For example, the timelessness of the Wheeler-DeWitt equation can be seen as resulting from using Jacobi's principle to define the dynamics of 3-geometries through superspace.…

This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…

The article under discussion, titled "Climbing Escher's stairs: A way to approximate stability landscapes in multidimensional systems" (doi: 10.1371/journal.pcbi.1007788), has captured our attention due to important methodological…