Related papers: Dynamics of a 3D Elastic String Pendulum
A new model for computer simulation of solids, composed of bonded rigid body particles, is proposed. Vectors rigidly connected with particles are used for description of deformation of a single bond. The expression for potential energy of…
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the…
This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic…
This paper considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape…
In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as…
Collisions play an important role in many aspects of the physics of musical instruments. The striking action of a hammer or mallet in keyboard and percussion instruments is perhaps the most important example, but others include reed-beating…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
We present and analyse a numerical method for understanding the low-inertia dynamics of an open, inextensible viscoelastic rod - a long and thin three dimensional object - representing the body of a long, thin microswimmer. Our model allows…
In the present paper we describe the dynamics of the revised rigid body, the dynamics of the rigid body with distributed delays and the dynamics of the fractional rigid body. We analyze the stationary states for given values of the rigid…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
The systematic errors due to the practical implementation of the Contact Dynamics method for simulation of dense granular media are examined. It is shown that, using the usual iterative solver to simulate a chain of rigid particles,…
We consider the numerical computation of a variational problem that arises from materials science. The target functional is a type of elastic energy that is influenced by obstacles and adhesion. Owing to its strong nonlinearity and…
Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…