相关论文: An Induced Representation Method for Studying the …
We give a self-contained modern linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. Starting with the mathematical description of the dynamics of the system, we form the linear…
We construct a new static solution to the 5D Einstein-Maxwell equations describing a static black hole surrounded by a non-rotating dipole black ring. The configuration is kept in equilibrium by an external magnetic field interacting with…
We investigate the stability properties of a multi-converter power system model, defined on a high-order manifold. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of AC…
The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10 that…
Here we demonstrate how Saturn could create its rings by itself, with the additional action of its axisymmetric magnetic field once appeared. A new mechanism for the origin of Saturn's rings is proposed for the first time. It includes the…
Let $D_n$ be the dihedral group with $2n$ elements, and suppose $n$ is greater than one. We call ring system a finite $D_n$-symmetric set of points in $\mathbb{R}^2$. Ring systems have been used as models for planets surrounded by rings,…
As it has already done for Earth, the sun, and the stars, seismology has the potential to radically change the way the interiors of giant planets are studied. In a sequence of events foreseen by only a few, observations of Saturn's rings by…
Seismology allows for direct observational constraints on the interior structures of stars and planets. Recent observations of Saturn's ring system have revealed the presence of density waves within the rings excited by oscillation modes…
In his 1856 Adams Prize essay, James Clark Maxwell demonstrated that Saturn's rings cannot be comprised of a uniform rigid body. This is a consequence of the two-body gravitational interaction between a ring and planet resulting in…
We present a new stationary, asymptotically flat solution of 5D Einstein-Maxwell gravity describing a Saturn-like black object: a rotating black hole surrounded by a rotating dipole black ring. The solution is generated by combining the…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and…
Maxwell's investigations into the stability of Saturn's rings provide one of the earliest analyses of the dynamics of astrophysical discs. Current research in planetary rings extends Maxwell's kinetic theory to treat dense granular gases of…
In a pioneering exposition of mathematical astronomy for the public, Sir John Herschel attributed the stability of the ring of Saturn to its being eccentric with respect to the planet and lopsided (asymmetric in mass) by a minute amount.…
Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing Black Saturn: a spherical black hole surrounded by a black ring. Angular momentum keeps the configuration in…
In this paper, we introduce a simplified model to understand the location of Saturn's F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic $J_2$, the…
Plasma rotation plays a large role in determining the size and shape of Saturn's disc-like magnetosphere. A magnetosphere more confined to the equator in the polar regions is expected as a result of the interaction between this type of…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by…
Spacecraft observations of Saturn's rings show evidence of an active aggregation-disaggregation process triggered by periodic influences from the nearby moons. This leads to clumping and break-up of the ring particles at time-scales of the…