Related papers: Modelisation of a rolling disk with Sympy
We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals,…
We find equations of particle motion from the point of view of observer on a rotating disk, and demonstrate that a particle moving along a rotating disk is influenced by forces arising from geometry. They can be considered as analogs of the…
In this paper, we investigate the theoretical possibility that a Lagrangian fixed point, when applied to cosmological models, can drive dynamical evolution towards a bouncing universe. We analyze the physics of a Lagrangian fixed point…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a…
In this paper we briefly discuss the ways in which angular momentum transport is included in simulations of non-self-gravitating accretion disks, concentrating on disks in close binaries. Numerical approaches fall in two basic categories;…
In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…
In this paper we present a Lagrangian method that allows the physical degree of freedom count for any Lagrangian system without having to perform neither Dirac nor covariant canonical analyses. The essence of our method is to establish a…
An exact analytical method for determining the Lagrangian velocity correlation and the diffusion coefficient for particles moving in a stochastic velocity field is derived. It applies to divergence-free 2-dimensional Gaussian stochastic…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction…
A system of equations, describing the evolution of electromagnetic fields, is introduced and discussed. The model is strictly related to Maxwell's equations. As a matter of fact, the Lagrangian is the same, but the variations are subjected…
This article illustrates the role of friction on the motion of a rolling sphere on pedagogical example. We use a parabolic support rotating around it axis to study the static equilibrium positions of a single sphere. Due to the particular…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition,…