Related papers: Analytical solution of the Euler-Poinsot problem
In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
This paper is devoted to the analysis of random motions on the line and in the space R^d (d > 1) performed at finite velocity and governed by a non-homogeneous Poisson process with rate \lambda(t). The explicit distributions p(x,t) of the…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
In this thesis we present partial progress towards the dynamic formation of black holes in the four-dimensional Einstein vacuum equations from Christodoulou's short-pulse ansatz. We identify natural scaling in a putative solution metric and…
We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolution…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
In this paper, the smooth solution of the physical vacuum problem for the one dimensional compressible Euler equations with time-dependent damping is considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder continuous.…
This manuscript develops a novel understanding of non-polar solutions of the discrete Painlev\'e I equation (dP1). As the non-autonomous counterpart of an analytically completely integrable difference equation, this system is endowed with a…
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution.…
We are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description…
This paper presents a new geometric and recursive algorithm for analytically computing the forward dynamics of heavy-duty parallel-serial mechanisms. Our solution relies on expressing the dynamics of a class of linearly-actuated parallel…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
This paper presents solutions to the following two common quaternion attitude estimation problems: (i) estimation of attitude using measurement of two reference vectors, and (ii) estimation of attitude using rate measurement and measurement…