Related papers: Lie Symmetry Analysis for Cosserat Rods
The Conclusive Theorem has been established to determine the dependence of the three-axes positive-definite Finsleroid metric functions $F$ on the Finsleroid azimuthal angle $\theta$ in the three-dimensional case $N=3$, provided that the…
The paper presents a constraint-based collision model for Cosserat rods, able to handle dynamic or static contact between a large number of highly flexible structures. The model provides the required collision impulses prior to updating the…
Soft robots have many advantages over rigid robots thanks to their compliant and passive nature. However, it is generally challenging to model the dynamics of soft robots due to their high spatial dimensionality, making it difficult to use…
The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous…
One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…
We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…
We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes…
In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's…
We rigorously derive an effective bending model for elastoplastic rods starting from three-dimensional finite plasticity. For the derivation we lean on a framework of evolutionary $\Gamma$-convergence for rate-independent systems. The main…
The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…
An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded…
We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled…
This paper introduces a Cosserat rod based mathematical model for modeling a self-controllable variable curvature soft continuum robot. This soft continuum robot has a hollow inner channel and was developed with the ability to perform…
We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order…
Understanding looping probabilities, including the particular case of ring-closure or cyclization, of fluctuating polymers (eg DNA) is important in many applications in molecular biology and chemistry. In a continuum limit the configuration…