Related papers: Energy-Preserving Integrators Applied to Nonholono…
In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system,…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove…
We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that…
We consider nonholonomic Chaplygin systems and associate to them a $(1,2)$ tensor field on the shape space, that we term the gyroscopic tensor, and that measures the interplay between the non-integrability of the constraint distribution and…
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved…
We consider minimum energy optimal control problem with time dependent Lagrangian on the nonholonomic integrator and and find the analytical solution using Sturm-Liouville theory. Furthermore, we also consider the minimum energy problem on…
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly,…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
The long-time behaviour of splitting integrators applied to nonlinear Schr\"odinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserved on long time intervals. The analysis includes all…
Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical…