The U (n) free rigid body: Integrability and stability analysis of the equilibria

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In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wea ...

Purpose: To develop a self-navigated motion compensation strategy for 3D radial MRI that can compensate for continuous head motion by measuring rigid body motion parameters with high temporal resolution from the central k-space acquisition point (self-enco ...

The progress towards intelligent systems and digitalization relies heavily on the use of automation technology. However, the growing diversity of control objects presents significant challenges for traditional control approaches, as they are highly depende ...

Many problems in robotics are fundamentally problems of geometry, which have led to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra, and d ...

Small-scale turbomachinery is increasingly used in carbon-free energy conversion systems, such as commercial or domestic scale heat pumps, fuels cells for transportation and waste heat recovery. The usage of aerodynamic bearings allows the design of compac ...

State-dependent dynamical systems (DSs) offer adaptivity, reactivity, and robustness to perturbations in motion planning and physical human-robot interaction tasks. Learning DS-based motion plans from non-linear reference trajectories is an active research ...

We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...

Incipient valley formation in mountainous landscapes is often associated with their presence at a regular spacing under diverse hydroclimatic forcings. Here we provide a formal linear stability theory for a landscape evolution model (LEM) representing the ...

Pulsatile jet propulsion is a highly energy-efficient swimming mode used by various species of aquatic animals that continues to inspire engineers of underwater vehicles. Here, we present a bio-inspired jet propulsor that combines the flexible hull of a je ...

We study a gravity-driven viscous flow coating a vertical cylindrical fibre. The destabilisation of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh-Plateau and Kapitza instabilities in the l ...

The global linear stability of a water drop on hot nonwetting surfaces is studied. The droplet is assumed to have a static shape and the surface tension gradient is neglected. First, the nonlinear steady Boussinesq equation is solved to obtain the axisymme ...

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

The dynamic behavior of spiral-grooved gas bearing supported four degrees-of-freedom (DOF) rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space ...

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i. ...

This study presents a general approach to the topology design of tensegrities with rigid bodies. To the best of the authors' knowledge, all existing topology design methods of tensegrities focus on tensegrities that only consist of members carrying axial f ...

Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of ...

A multimaterial inkjet printing method for integrated soft multifunctional machines is reported, combining dense arrays of electrostatic actuators, multilayer electrical routing, and complex networks of microfluidic channels in one printing process. Most a ...

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system ...

The U (n) free rigid body: Integrability and stability analysis of the equilibria

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Stability: a search for structure

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Rapid motion estimation and correction using self-encoded FID navigators in 3D radial MRI

Data-driven Methods for Control: from Linear to Lifting

Geometric Algebra for Optimal Control With Applications in Manipulation Tasks

Numerical and experimental investigation of spiral-grooved gas journal bearings

Locally active globally stable dynamical systems: Theory, learning, and experiments

On minimal tilting complexes in highest weight categories

Inception of Regular Valley Spacing in Fluvial Landscapes: A Linear Stability Analysis

Lagrangian analysis of bio-inspired vortex ring formation

Whirling instability of an eccentric coated fibre

Buoyancy-driven convection of droplets on hot nonwetting surfaces

Spherical birational sheets in reductive groups

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

Second-order adjoint-based sensitivity for hydrodynamic stability and control

Topology design of general tensegrity with rigid bodies

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Inkjet Printing of Complex Soft Machines with Densely Integrated Electrostatic Actuators

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion