Related papers: Time-Dependent Lagrangian Biomechanics
The global time in Geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of…
In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
We describe the structure of relaxation for a steadily driven macroscopic body. The time-evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing the dynamical…
This paper presents a novel recurrent neural network-based method to construct a latent motion manifold that can represent a wide range of human motions in a long sequence. We introduce several new components to increase the spatial and…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…
Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…
The aim of this paper is to geometrize time dependent Lagrangian mechanics in a way that the framework of second order tangent bundles plays an essential role. To this end, we first introduce the concepts of time dependent connections and…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…
Human pose, action, and motion generation are critical for applications in digital humans, character animation, and humanoid robotics. However, many existing methods struggle to produce physically plausible movements that are consistent…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
We present a constructive derivation of a time-dependent deformation functional theory -- a collective variable approach to the nonequalibrium quantum many-body problem. It is shown that the motion of infinitesimal fluid elements (i.e. a…
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…
We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…