Related papers: Virtual Displacement in Lagrangian Dynamics
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
In this paper we study a problem in oscillations wherein the assumed modes method offers some analytical and theoretical peculiarities. Specifically, we study small in-plane oscillations of a slack catenary, or a sagging inextensible chain…
We investigate vector contributions to the Lagrangian of $\Lambda_3-$massive gravity in the decoupling limit, the less explored sector of this theory. The main purpose is to understand the stability of maximally symmetric %self-accelerating…
We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
Useful definitions and properties pertaining to static granular packings, in which a contact network is able to support externally applied forces and maintain equilibrium for varying loads, are reviewed and discussed. It is explained how…
Vehicle Routing Problems (VRPs) in real-world applications often come with various constraints, therefore bring additional computational challenges to exact solution methods or heuristic search approaches. The recent idea to learn heuristic…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental…
We model spacetime foam by a gas of virtual wormholes. For a free scalar field we derive the effective Lagrangian which accounts for the interaction with spacetime foam and contains two additional non-local terms. One term describes the…
We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…