Prograde and retrograde precession of a fluid-filled cylinder

We numerically study precession driven flows in a cylindrical container whose nutation angle varies between 60 and 90 degrees for prograde and retrograde precession. For prograde precession we observe sharp transitions between a laminar and a turbulent flow state with low and high geostrophic axisymmetric flow components related with a centrifugal instability, while for retrograde precession a rather smooth transition between a low state and a high state occurs. At the same time prograde and perpendicular precession shows an abrupt breakdown of the flow directly excited by the forcing mechanism, which is not the case for retrograde motion. We characterize the corresponding flow states in terms of the directly driven, non-axisymmetric Kelvin mode, the axisymmetric geostrophic mode, and an axisymmetric poloidal flow which is promising for precession-driven dynamo action. The latter issue is discussed with particular view on an optimal parameter choice for the DRESDYN dynamo project.

An Underwater Vector Propulsion Device Based on the RS+2PRS Parallel Mechanism and Its Attitude Control Algorithm

In order to overcome the disadvantages of some existing autonomous underwater vehicles (AUVs), such as actuator extraposition and degree-of-freedom (DOF) redundancy, a 2-DOF vector propeller propulsion system with built-in actuator based on the deficient DOF parallel mechanism is proposed. The RS+2PRS (Revolute-Spherical+ Prismatic-Revolute-Spherical) parallel mechanism is used as the main structure, and the driving parts are placed in the interior of the AUV cabin, which is beneficial to the sealing and protection of the propulsion system. In addition, the motion parameters decoupling shows that the two independent parameters are the precession angle and the nutation angle of the propeller installation platform. Therefore, the attitude control algorithm uses two prismatic joints as driving units to establish the nonlinear mapping model with the two Euler attitude angles. In the end, the simulation analysis and the real device are used to verify the feasibility of the attitude control algorithm and the in situ adjustment function of the propeller, which lays the theoretical foundation for engineering applications in the future.

SEMI STABLE FLIGHT OF SUPERSONIC MORTAR PROJECTILE

Significantly large dispersion of projectiles was observed at firing a specific type of a supersonic mortar projectile being devel-oped in the frame of RAK ANUNICJA program. The flying paths, parameters and reasons of falling points dispersion were determined for tested projectiles with a model of external ballistics describing the projectile as a rigid body. Analysis of received results has indicated that the dispersion was not caused by an aerodynamic jump but by an effect which has not been described yet in the literature and is named here as “projectile’s semi-stable flight”. The paper includes a description of the effect with reasons and parameters affecting its occurrence, and a method for determination of the equilibrium nutation angle which plays a key role in this effect.

Estimates of the average angular velocity of the precession of Lagrange's top

Guaranteed upper and lower estimates of the increment in the precession angle per nutation angle period under nondegenerate motions of a Lagrange top have been obtained in the article.

Stability of LevitronTM revisited

This note discusses some issues related to stability of stationary motion of hovering magnetized top in a homogeneous magnetic field. Stability of synchronous motion is analyzed using the simplified model in which the hovering motion of the center of mass is ignored. Stability boundaries are derived using Lyapunov direct method. In particular, it is shown that, for a given angle ? between magnetic moment dipole and principal axis of the top, there is an interval of stationary values of nutation angle ??0 for which the stationary synchronous motion is stable.

Triadic resonances in precessing rapidly rotating cylinder flows

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

Application of the Steady-state Variable Nutation Angle Method for Faster Determinations of Long T1S–-an Approach Useful for the Design of Hyperpolarized Mr Molecular Probes

In the dissolution-dynamic nuclear polarization technique, molecular probes with long T1s are preferred. 13C nuclei of small molecules with no directly bonded protons or sp313C nuclei with proton positions substituted by deuterons may fulfill this requirement. The T1 determination of such new molecular probes is crucial for the success of the hyperpolarized observation. Although the inversion-recovery approach remained by and large the standard for T1 measurements, we show here that the steady-state variable nutation angle approach is faster and may be better suited for the determination of relatively long T1s in thermal equilibrium. Specifically, the T1 of a new molecular probe, [uniformly labeled (UL)-13C6, UL-2H8]2-deoxy-d-glucose, is determined here and compared to that of [UL-13C6, UL-2H7]d-glucose.