Related papers: Variational Principle for Planetary Interiors
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
The four equations of stellar structure are reformulated as two alternate pairs of variational principles. Different thermodynamic representations lead to the same hydromechanical equations, but the thermal equations require, not the…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
This paper develops some mathematical models arising in behavioral sciences, particularly in psychology, which are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational…
The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
We advance a famous principle - causality principle - but under a new view. This principle is a principium automatically leading to most fundamental laws of the nature. It is the inner origin of variation, rules evolutionary processes of…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…