Related papers: Kovalevskaya top -- an elementary approach
This short note contains elementary evaluations of some Euler sums.
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most…
We consider an integrable three-dimensional system of ordinary differential equations introduced by S.V. Kovalevskaya in a letter to G. Mittag-Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two…
The structure of integral manifolds in the Kovalevskaya problem of the motion of a heavy rigid body about a fixed point is considered. An analytic description of a bifurcation set is obtained, and bifurcation diagrams are constructed. The…
We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B2 integrable lattice.…
The main solutions in sense of Kantorovich of nonlinear Volterra operator-integral equations are constructed. Convergence of the successive approximations is established through studies of majorant integral and majorant algebraic equations.…
This note is concerned with the linear matrix equation $X = AX^\top B + C$, where the operator $(\cdot)^\top$ denotes the transpose ($\top$) of a matrix. The first part of this paper set forth the necessary and sufficient conditions for the…
We descibe a number of dynamical systems that are generalizations of S. Kowalevskaya system and admit the Lax representation.
Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its expansions. Exact Euler…
The authors propose and analyze a well-posed numerical scheme for a type of ill-posed elliptic Cauchy problem by using a constrained minimization approach combined with the weak Galerkin finite element method. The resulting Euler-Lagrange…
In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov's accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity…
This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…
Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…
We present in this article a general approach (in the form of recommendations and guidelines) for tackling Diophantine equation problems (whether single equations or systems of simultaneous equations). The article should be useful in…
This paper provides a detailed description of various reduction schemes in rigid body dynamics. Analysis of one of such nontrivial reductions makes it possible to order the cases already found and to obtain new generalizations of the…
We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing…
Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver algorithms are discussed. New…
Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In…