Related papers: Modelisation of a rolling disk with Sympy
In this paper we construct a solution of the two-dimensional problem of the elasticity theory (plane deformation) on pressing of the flat stamp in the rectangular plate by using the symbolic method and the exact solution of the harmonic…
Free spinor fields, with spin 1/2, are explored in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation operators and on their base…
A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of…
A class of non-strictly hyperbolic systems of quasilinear equations with oscillatory solutions of the Cauchy problem, globally smooth in time in some open neighborhood of the zero stationary state, is found. For such systems, the period of…
This paper discusses the free vibration of elastic spherical structures in the presence of an externally unbounded acoustic medium. In this vibration, damping associated with the radiation of energy from the confined solid medium to the…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…
We propose a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity. Matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A phase space…
Using the relativistic electrodynamics of continuous media formalism and main relativistic quantum field theory principles the covariant Lagrangian of electromagnetic field interaction with polarizable 1/2-spin particles have been obtained.…
We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and…
Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle alpha of the coin to the table decreases, while the angular velocity Omega of the point of…
The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by…
The aim of this paper is to write explicit expression in terms of a given principal connection of the Lagrange-d'Alembert-Poincar\`{e} equations in several stages. This is obtained by using a reduced Lagrange-d'Alembert's Principle in…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
Force-free magnetic fields are important in many astrophysical settings. Determining the properties of such force-free fields -- especially smoothness and stability properties -- is crucial to understanding many key phenomena in…
The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of…
The theory of freely-propagating massless higher spins is usually formulated via gauge fields and parameters subject to trace constraints. We summarize a proposal allowing to forego them by introducing only a pair of additional fields in…