Escherart统一理论的变分表述

相对论流体力学的变分公式

A variational formulation of relativistic hydrodynamics

我们结合陶伯和雷的变分方法到另一个简单的制定完美的流体的相对论流体动力学。

非完整约束系统的变分形式

On the variational formulation of systems with non-holonomic constraints

在作者以前的一篇文章中，它表明，人们可以有效地给一个变分制定的非保守力学系统开始与第一变分功能，而不是一个行动的功能。在这篇文章中，它表明，这种相同的方法也将允许一个给一个变分制定系统的非完整约束。关键是在公式中使用一个自适应的非完整局部标架场，这意味着用协变导数代替普通导数。然后将该方法应用于平面上无滑动或无摩擦的垂直圆盘滚动的情况。

辛非对易力学的变分形式

A Variational Formulation of Symplectic Noncommutative Mechanics

非对易物理学的标准知识是使用动力学系统的一阶变分描述来探测空间非对易性及其在相空间动力学中的后果。由于最终目标是理解固有的空间非对易性，我们基于我们以前工作的结果[14]，提出了位形空间中非对易动力系统的变分原理。我们希望这种位形空间的变分形式能有助于阐明经典和量子非对易空间的某些整体性质和动力学性质的定义。

Griffiths Variational Multisymplectic Formulation for Lovelock Gravity

This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.

Flux-variational formulation of relativistic perfect fluids

We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity equations are obtained quite directly.

A Hamiltonian Formulation of Causal Variational Principles

Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in space-time. After generalizing causal variational principles to a class of lower semi-continuous Lagrangians on a smooth, possibly non-compact manifold, the corresponding Euler-Lagrange equations are derived. In the first part, it is shown under additional smoothness assumptions that the space of solutions of the Euler-Lagrange equations has the structure of a sympl…