Related papers: Understanding d'Alembert's principle: System of Pe…
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR…
The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…
Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus…
Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws, such as the non-increase of entanglement under local operations,…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the…
The Lagrange--Poincar\'e equations for the mechanical system describing the motion of a scalar particle on a Riemannian manifold with a given free and isometric action of a compact Lie group is obtained. In an arising principle fibre…
It is demonstrated how all the mechanical equations of classical electrodynamics (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
In this paper, we prove that D'Alembert-Lagrange principle for point masses using Lagrange-Mach's mechanical construction yields a weighted balancing condition of unit vectors in $\mathbb{E}^{3}.$
We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero…
The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
It is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($\Lambda$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time…
This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
The paper investigates a systematic approach to modeling in nonequilibrium thermodynamics by focusing upon the notion of interconnections, where we propose a novel Lagrangian variational formulation of such interconnected systems by…