Related papers: Time-Dependent Lagrangian Biomechanics
The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather…
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…
In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the…
In Continuum Mechanic a simple material body $\mathcal{B}$ is represeted by a three-dimensional differentiable manifold and the configuration space is given by the space of embeddings $Emb \left( \mathcal{B} , \mathbb{R}^{n} \right)$. We…
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Motion prediction is a classic problem in computer vision, which aims at forecasting future motion given the observed pose sequence. Various deep learning models have been proposed, achieving state-of-the-art performance on motion…
The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear…
A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator…
We study the geometric phases of nonlinear elastic $N$-rotors with continuous rotational symmetry. In the Hamiltonian framework, the geometric structure of the phase space is a principal fiber bundle, i.e., a base, or shape…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
This paper addresses the critical and challenging task of developing emulators for simulating human operational motions in industrial workplaces. We conceptualize human motion as a sequence of human body shapes and develop statistical…
Human motion prediction aims to forecast future human poses given a prior pose sequence. The discontinuity of the predicted motion and the performance deterioration in long-term horizons are still the main challenges encountered in current…