Related papers: Inertial control of a spinning flat disk
This paper investigates the dynamics of closed vortex filaments in $\R^3$ governed by the Localized Induction Equation. Recently, Aiki and Higaki (2026) established the nonlinear orbital stability of circular vortex filaments under…
This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…
We present a simple example in which the importance of the inertial effects of stress is evident. The system is an insulating solid narrow disc whose faces are uniformly charged with charges of equal magnitude and opposite signs. The motion…
Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured…
We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces a compressive orthoradial stresses which leads to a wrinkling instability above a critical threshold of the…
This paper proposes a Lagrangian approach to find the state equations of a disk rolling on a plane without friction. The approach takes advantage of a symbolic computation to simplify the reasoning.
The dark matter accretion theory (around a central body) of the author on the basis of his 5-dimensional Projective Unified Field Theory (PUFT) is applied to the orbital motion of stars around the center of the Galaxy. The departure of the…
We discuss the rolling, without slip and without twist, of Stiefel manifolds equipped with $\alpha$-metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely by investigating…
The elliptical instability is a generic instability which takes place in any rotating flow whose streamlines are elliptically deformed. Up to now, it has been widely studied in the case of a constant, non-zero differential rotation between…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…
In-Orbit Servicing and Active Debris Removal require advanced robotic capabilities for capturing and detumbling uncooperative targets. This work presents a hierarchical control framework for autonomous robotic capture of tumbling objects in…
We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated,…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients.…
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC)…
We develop a functional-analytical machinery for studying the quadratic regulator problem arising from spectra perturbations of infinite-dimensional dynamical systems. In particular, we are interested in applications to inertial manifolds…
This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with…
This paper presents the concept of a tethered variable inertial attitude control mechanism for a modular jumping-limbed robot designed for planetary exploration in low-gravity environments. The system, named SPLITTER, comprises two sub-10…
The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal…