Related papers: Action principle for Numerical Relativity evolutio…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the…
A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard…
We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian, as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be…
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties…
Studies of new hyperbolic systems for the Einstein evolution equations show that the ``slicing density'' $\alpha(t,x)$ can be freely specified while the lapse $N = \alpha g^{1/2}$ cannot. Implementation of this small change in the…
The gauge invariant minimal couplings for a class of relativistic free matter fields with global symmetry (related to usual charge conservation) have been obtained by incorporating an iterative Noether mechanism. Non-relativistic reduction…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge…
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
We study the evolution equation for magnetic energy density for a non-relativistic magnetized plasma in the (Lagrangian) reference frame comoving with the electron bulk velocity. Analyzing the terms that arise due to the ideal electric…
Geometric representations of solutions provides intuitive physical insights. To which end studying dynamics of Quantum systems via $su (n)$ Lie algebra proves to be convenient way of obtaining geometric solution. In this paper link is…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for…