Related papers: Dynamics of Connected Rigid Bodies in a Perfect Fl…
This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…
This paper presents an analytical model and a geometric numerical integrator for a rigid body connected to an elastic string, acting under a gravitational potential. Since the point where the string is attached to the rigid body is…
This paper presents an analytical model and a geometric numerical integrator for a tethered spacecraft model that is composed of two rigid bodies connected by an elastic tether. This model includes important dynamic characteristics of…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
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…
The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…
We present a novel framework for rigid body dynamics in ambient media, such as air or water, enabling accurate motion prediction of objects without requiring computational fluid dynamics simulations. Our method computes the added mass of…
This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…
Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the coordinate singularities associated with local coordinate…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…
Robotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer's hydrodynamics in order to…
This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D)…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
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 this paper, we derive the continuous space-time equations of motion of a three-dimensional geometrically exact rod, or the Cosserat rod, incorporating planar cross-sectional deformation. We then adopt the Lie group variational integrator…
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…