相关论文: Lie Group Variational Integrators for the Full Bod…

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

We consider a hierarchy of classical Liouville completely integrable models sharing the same (linear) $r$--matrix structure obtained through an $N$--th jet--extension of $\mathfrak{su}(2)$ rational Gaudin models. The main goal of the…

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…

Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them.…

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…

The Laplace equation in the two-dimensional Euclidean plane is considered in the context of the inverse stereographic projection. The Lie algebra of the conformal group as the symmetry group of the Laplace equation can be represented solely…

We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…

This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on the product of an arbitrary number of two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations are developed in a…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…

A generalization of non-Abelian gauge theories of compact Lie groups is developed by gauging the non-compact group of volume-preserving diffeomorphisms of a $D$-dimensional space R^D. This group is represented on the space of fields defined…

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…

We consider the Regge-Teitelboim model for a relativistic extended object embedded in a fixed background Minkowski spacetime, in which the dynamics is determined by an action proportional to the integral of the scalar curvature of the…

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,…

Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor-coefficients of the…

We present a fully covariant transport framework for Molecular Dynamics that enables a consistent description of the evolution of relativistic N-body systems. For the first time, we derive relativistic equations of motion incorporating both…

Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…

In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the…

One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…

We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the…