Related papers: Novel solvable many-body problems
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.
A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…
Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established. More precisely, a concrete interval of positive parameters, for which the treated…
For the first time a method is devised for non-iterative modeling of motion of a radiating, electrified pointlike mass that has an internal structure. New, supplementary kinetic constants of accelerated charged particles are defined, that…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
A new solvable many-body problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.
Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are…
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…