Related papers: Dynamics of a 3D Elastic String Pendulum

We propose to use the properties of the Lie algebra of the angular momentum to build symplectic integrators dedicated to the Hamiltonian of the free rigid body. By introducing a dependence of the coefficients of integrators on the moments…

This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…

We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We…

The paper presents a new observer for tilt estimation of a 3-D non-rigid pendulum. The system can be seen as a multibody robot attached to the environment with a ball joint. There is no sensor for the joint position of the sensor. The…

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into the space of a constant curvature. It is shown that the rigid…

We present a numerical solution of the nonlinear differential equation for a pendulum with an elastic string on the rotating Earth, for different values of string stiffness at different geographic latitudes.

We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational…

It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…

This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference…

Previous work introduced a lower-dimensional numerical model for the geometric nonlinear simulation and optimization of compliant pressure actuated cellular structures. This model takes into account hinge eccentricities as well as…

This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible…

In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…

Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited…

The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…

We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…

Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…

We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…

Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist, and in this work we focus on Runge--Kutta--Munthe--Kaas methods. First, we briefly…