Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces

<p style='text-indent:20px;'>This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [<xref ref-type="bibr" rid="b26">26</xref>] for submanifolds of an Euclidean space. We also prove some important properties of these rolling maps. After presenting the general framework, we analyse the particular rolling of hyperquadrics embedded in pseudo-Euclidean spaces. The central topic is the rolling of a pseudo-hyperbolic space over the affine space associated with its tangent space at a point. We derive the kinematic equations, as well as the corresponding explicit solutions for two specific cases, and prove the existence of a rolling map along any curve in that rolling space. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. Finally, for the central theme, we write the kinematic equations as a control system evolving on a certain Lie group and prove its controllability. The choice of the controls corresponds to the choice of a rolling curve.</p>

Research on rolling stability of the flexible waverider based on computational fluid dynamics/computational structural dynamics/rigid body dynamics coupling methodology

The shape of hypersonic aircrafts represented by waveriders is becoming more slender and flatter, thereby greatly reducing the structural rigidity. This innovation is applied to satisfy the demand of long-range flight. The rolling stability of the waveriders is poor due to the slender shape. Therefore, the effect of the elastic deformation on the rolling stability cannot be ignored. The effect of the elastic deformation on the stability of rolling and forced pitching/free rolling coupling motions of the waveriders is studied through computational fluid dynamics (CFD)/computational structural dynamics (CSD)/rigid body dynamics (RBD) coupling methodology. Comparison results of numerical simulation indicate that the elastic deformation of the structure increases the local angle of attack, thereby enhancing the static stability of the waveriders. The rolling motion of the waveriders changes from point attractor to periodic attractor when the vibration velocity due to elastic deformation is considered. The rolling oscillation frequency of the flexible model is higher than that of the rigid model. For the forced pitching/free rolling motion, stability theory based on the rigid body hypothesis is unsuitable when the elastic effect is taken into consideration.

Downstroke and upstroke conflict during banked turns in butterflies

For all flyers, aeroplanes or animals, making banked turns involve a rolling motion which, due to higher induced drag on the outer than the inner wing, results in a yawing torque opposite to the turn. This adverse yaw torque can be counteracted using a tail, but how animals that lack tail, e.g. all insects, handle this problem is not fully understood. Here, we quantify the performance of turning take-off flights in butterflies and find that they use force vectoring during banked turns without fully compensating for adverse yaw. This lowers their turning performance, increasing turn radius, since thrust becomes misaligned with the flight path. The separation of function between downstroke (lift production) and upstroke (thrust production) in our butterflies, in combination with a more pronounced adverse yaw during the upstroke increases the misalignment of the thrust. This may be a cost the butterflies pay for the efficient thrust-generating upstroke clap, but also other insects fail to rectify adverse yaw during escape manoeuvres, suggesting a general feature in functionally two-winged insect flight. When lacking tail and left with costly approaches to counteract adverse yaw, costs of flying with adverse yaw may be outweighed by the benefits of maintaining thrust and flight speed.

Untethered Origami Worm Robot with Diverse Multi-Leg Attachments and Responsive Motions under Magnetic Actuation

Nowadays, origami folding in combination with actuation mechanisms can offer deployable structure design, yield compliance, and have several properties of soft material. An easy complex folding pattern can yield an array of functionalities in actuated hinges or active spring elements. This paper presents various cylinder origami robot designs that can be untethered magnetically actuated. The different designs are analyzed and compared to achieve the following three types of motion: Peristaltic, rolling, and turning in different environments, namely, board, sandpaper, and sand. The proposed origami robot is able translate 53 mm in peristaltic motion within 20 s and is able to roll one complete cycle in 1 s and can turn ≈ 180∘ in 1.5 s. The robot also demonstrated a peristaltic locomotion at a speed of ≈2.5 mm s−1, ≈1.9 mm s−1, and ≈1.3 mm s−1 in board, sandpaper, and sand respectively; rolling motion at a speed of 1 cycle s−1, ≈0.66 cycles s−1, and ≈0.33 cycles s−1 in board, sandpaper, and sand respectively; and turning motion of ≈180∘, ≈83∘, and ≈58∘ in board, sandpaper, and sand respectively. The evaluation of the robotic motion and actuation is discussed in detail in this paper.

Utilization of the phyphox application (physical phone experiment) to calculate the moment of inertia of hollow cylinders

Experiments have been carried out on determining the value of the moment of inertia of a hollow cylinder. This study aims to analyze the value of the moment of inertia with variations in the radius of the hollow cylinder using the Phyphox Application (Physical Phone Experiment). This research is experimental. The tools and material used area 1-meter longboard, three hollow cylinders with different radius sizes but the same mass, smartphone, laptop, caliper, and balance.The experiment of rolling motion on a hollow cylinder on an inclined plane is assisted by data processing in a Phyphoxapplication. From the experiment, the result of the moment of inertia value from data processing is 4.89 x 10-4kg.m2, 9.82 x 10-4kg.m2, 12.4 x10-4kg.m2. This research can be used as a teacher reference in teaching the topic of moments of inertia in physics learning at school. This is highly recommended for distance learning during the pandemic so that mastery of concepts is maximized. Further research is suggested that it can be tried to use other materials with other types of rigid bodies to find the moment of inertia. Further references on digital application media to assist learning are also needed considering the dynamic development of technology.

Flow and Heat Transfer of Supercritical Co2 in a Vertical Tube Under Ocean Rolling Motion

In order to explore the fluid flow and heat transfer features of supercritical fluids used in Brayton cycle for waste-heat utilization of marine gas turbines, the effects of ocean rolling motion on thermo-fluidic characteristics of supercritical carbon dioxide (SCO2) in a circular tube are computationally investigated based on a verified turbulence model. It can be found that at a given rolling period, compared to that under static condition, the time-averaged heat transfer capacity is improved by 7.9%, but the onset of the heat transfer recovery is delayed so that the range of the heat transfer deterioration becomes widened. Under the action of the inertial forces, the heat exchange between cooler/denser and warmer/lighter fluids is enhanced, a secondary circulation formed at t/tc = 0.325 and the maximum improvement of section-averaged heat transfer coefficient is 71% at this time. For various periods, the variation trend of time-averaged heat transfer coefficient for SCO2 shows a parabolic, which is distinguishing from conventional fluids. A polarization phenomenon for instantaneous thermal performance can be observed under severe rolling. With rise of the layout height, the time-average heat transfer performance of tube increases monotonously, and the maximum increment is 10.64% in study range.

Numerical Investigation of Pool Boiling Under Ocean Condition with Lattice Boltzmann Simulation. Part Ⅱ: Rolling Condition

Rolling motion caused by ocean condition will induce more complicated inertial forces with their force directions changing all the time, which results more complex bubble behaviors and unique heat transfer characteristics. In this work, pool boiling under rolling condition is numerically simulated using multiple relaxation time phase change lattice Boltzmann method (LBM). Pool boiling patterns, boiling curve of time-averaged heat flux, transient heat flux and rolling effects on different pool boiling regions are investigated. The results show that pool boiling curve of time-averaged heat flux between rolling condition and static condition are not obvious until close to critical heat flux, and 9.3% higher CHF is achieved under rolling condition while worse heat transfer is discovered at film boiling. Moreover, distinct fluctuation of transient heat flux of pool boiling under rolling condition is found for all boiling regimes, and its variation pattern along with the rolling motion and bubble behavior is investigated. Furthermore, tangential inertial force caused by rolling motion has positive influence on heat transfer of pool boiling, while the centrifugal force has negative influence on heat transfer, since it is opposite to the gravity and hence decreases the buoyancy force. Besides, larger rolling amplitude and smaller rolling period will induce larger additional inertial forces, and thus make greater influences on the bubbles’ behavior and pool boiling heat transfer.