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The recent availability of digital traces from Information and Communications Technologies (ICT) has facilitated the study of both individual- and population-level movement with unprecedented spatiotemporal resolution, enabling us to better…
We study a one dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio-Baradat-Brenier, of the discrete Monge-Amp\`ere gravitational model, which describes the motion of interacting…
This paper presents thorough mathematical modeling, control law development, and simulation of virtual structure formations which are inspired by the characteristics of rigid bodies. The stable constraint forces that establish the rigidity…
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
The relationship between balance laws and the Principle of Virtual Work as well as the structure of contact interactions in continua remain foundational issues in Mechanics. In this work, we revisit these issues within the distributional…
It is proved by means of the dynamical effects of special relativity that velocity caused by accelerating process is not a relative concept. The influence of accelerating process should be considered in space-time theory. Besides the…
The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later…
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…
The derivation of the equations of motion for nonholonomic systems remains a central issue in analytical mechanics, primarily due to the tension between the d'Alembert-Lagrange differential principle and integral variational approaches.…
This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Neural networks are regarded as systems whose connections are Lagrangian variables, namely functions depending on…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
The definitions of gravitational work as well as work done by the total external force on a massive probe particle moving in generic spacetime backgrounds are proposed. These definitions are given in the form of scalar integrals and thus,…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
We discuss several aspects of the stress-energy tensor for a quantum scalar field in an inhomogeneous background, the latter being modeled by a variable mass. Using a perturbative approach, dimensional regularization and adiabatic…