Angular Velocity Research Articles

Multipoint Variable parameter compliant control of redundant manipulator based on the equivalent twin model of flexible contact dynamics

To elucidate the dynamic coupling mechanism involved in multipoint/arbitrary point contact during human–robot interactions with redundant manipulators, we introduce a compliant control strategy that adapts to variable parameters. This strategy is based on the flexible contact dynamic equivalent twin system for human–robot interactions. Using the Virtual Elastic Element Representation model for arbitrary point contact dynamics and leveraging the skeleton principle for contact force conversion, we construct a flexible contact dynamic equivalent twin system tailored for redundant manipulators with multipoint/arbitrary point contact capabilities. Within this system, we implement real-time adjustments to the impedance stiffness coefficient in conjunction with the virtual end velocity of the manipulator. We optimize the joint angular velocity of the manipulator while considering the motion allocation of redundant degrees of freedom. This optimization enables multipoint contact variable parameter compliance control for safe human–robot interactions. To validate our approach, we analyze the multipoint contact dynamic model of the redundant manipulator's interaction with humans and assess the feasibility of the variable parameter compliance control method using robot operating system simulations. Ultimately, we verify the effectiveness and practicality of our proposed compliance control method through simulation and experimental results.

Integrated modeling of anisotropic neutron yields of classical and spherical tokamaks

Estimations of counting rates of neutron spectrometers in experiments on controlled fusion with magnetic confinement, as well as calculations of energy resolved flux densities of fusion neutrons from plasma to the walls of a reactor require spatial integration of the local, usually anisotropic function of the neutron source. The integrated modeling consists of three main stages. First, sources of fast particles in beam- or wave-heated plasma are calculated. The next stage deals with spatial, energetic, and angular velocity distributions of plasma ions. Finally, double differential rate coefficients of nuclear fusion reactions are computed. This article describes calculations of spatial distributions of nuclear fusion reaction rates in classical and spherical tokamaks and the anisotropy of the neutron yield and spectra. The results are based on analytical formulas for energetic and angular distributions of the local source of fusion products in plasma. Examples of energetic spectral densities of neutron fluxes on first walls are presented, as well as energy resolved counting rates of collimated neutron spectrometers for perpendicular and tangential lines of sight.

Deformation analysis of ground and existing tunnel induced by overlapped curved shield tunneling

The deformation caused by tunnel excavation is quite important for safety, especially when it is adjacent to the existing tunnel. Nevertheless, the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate. The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory, Mindlin solution and Euler-Bernoulli-Pasternak model, subsequently validated through both finite element simulation and field monitoring. It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling. The longitudinal settlement distribution can be categorized into five areas, with the area near the tunnel surface experiencing the most dramatic settlement changes. The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure, especially when the turning radius is less than 30 times the tunnel diameter. The tunnel crown exhibits larger displacement than the tunnel bottom, resulting in a distinctive 'vertical egg' shape. Furthermore, an optimized overcutting mode is proposed, involving precise control of the extension speed and angular velocity of the overcutting cutter, which effectively mitigates ground deformation, ensuring the protection of the existing tunnel during the construction.

Nonideal Magnetohydrodynamic Instabilities in Protoplanetary Disks: Vertical Modes and Reflection Asymmetry

Magnetized disk winds and wind-driven accretion are an essential and intensively studied dispersion mechanism of protoplanetary disks (PPDs). However, the stability of these mechanisms has yet to be adequately examined. This paper employs semi-analytic linear perturbation theories under nonideal magnetohydrodynamics, focusing on disk models whose magnetic diffusivities vary by a few orders of magnitude from the disk midplane to its surface. Linear modes are distinguished by their symmetry with respect to the midplane. These modes have qualitatively different growth rates: symmetric modes almost always decay, while at least one antisymmetric mode always has a positive growth rate. This growth rate decreases faster than the Keplerian angular velocity with cylindrical radius R in the disk and scales steeper than R −5/2 in the fiducial disk model. The growth of antisymmetric modes breaks the reflection symmetry across the disk equatorial plane, and may occur even in the absence of the Hall effect. In the disk regions where fully developed antisymmetric modes occur, accretion flows appear only on one side of the disk, while disk winds occur only on the other. This may explain the asymmetry of some observed PPD outflows.

Non-cooperative target recognition and relative motion estimation with inertial measurement unit assistance

This study investigated the problems of non-cooperative target recognition and relative motion estimation during spacecraft rendezvous maneuvers. A structure integrating an Inertial Measurement Unit (IMU) and a visual camera was presented. The angular velocity output of the IMU was used to calculate the motion trajectories of star points in multiple image frames, which can highlight the motion of non-cooperative targets with respect to the image background to improve the probability of target recognition. To solve the problem of target misidentification caused by new star points entering the field of view, a target-tracking link based on IMU prediction was introduced to track the position of the target in the image. Furthermore, a measurement model was constructed using the line-of-sight vector generated from target recognition, and the relative motion state was estimated using a Huber-based non-linear filter. Semi-physical and numerical simulations were performed to evaluate the effectiveness and efficiency of the proposed method.

Characteristics of deploying longitudinal folding wings with compound actuation

A mechanism has been developed to achieve rapid deployment of longitudinally folding wings by utilizing compound actuation from the firing powder and the compressive spring. A theoretical model based on rigid-body dynamics was first proposed to study the deployment characteristics of longitudinal folding wings under compound-driven effects. Subsequently, deployment experiments were conducted using a prototype to validate the theoretical model. It was observed that the folding wings are deployed in 11 ms. Further parametric analysis indicates that the mass of both the propellant and the locking rod has a positive effect on the deploying velocity. However, the angular moment of inertia of folding wings has a negative effect on the initial angular velocity. This work can be helpful for designing the folding wing structures of missiles and aircrafts.

Kinematic analysis on segment angle and angular velocities of recovery leg of world elite race walkers regarding race-walking judgement on world elite competition of athletics

Kinematic analysis on segment angle and angular velocities of recovery leg of world elite race walkers regarding race-walking judgement on world elite competition of athletics

Surface profile inspection for large structures with laser scanning

Fringe projection profilometry is a powerful tool that is widely applied to shape measurement of objects in engineering. Limited by the light intensity of the projection unit, this technique is difficult to be applied to surface inspection of large structures, especially in outdoor applications. In this study, a line laser source is selected as the light projection unit. The line laser beam is controlled to scan the surface with the predefined angular speed while a stationary imaging unit captures images. An image fusion strategy has been proposed to construct grating images with a constant phase shift, which facilitates full-field phase shifting in determination of the structural profile. The accuracy of the measurement method is discussed and compared with a commercial 3D laser scanner. The proposed technique has also been applied to the surface topography of the wind turbine blades. The experimental results show that the bulging defects on the surface of the wind turbine blade model are detectable, which shows the feasibility of the proposed method in characterization of surface profile on large structures.

The E × B magnetized plasma device (EMPD).

A plasma device has been created to study dynamic plasma coupling in an E × B-drifting magnetized plasma. The E × B magnetized plasma device is a 1.2m diameter by 2m long cylindrical chamber with two sets of Helmholtz coils in a mirror configuration. A steady-state axial hollow cathode source injects a plasma discharge in electrical contact with a floating conductor at a range that forms a unique axisymmetric equipotential surface or Virtual Cathode Lightsaber (VCL). The VCL generates two plasma populations streaming relative to one another providing a suitable environment for the investigation of dynamic plasma coupling. The plasma density, radial electric field, and plasma rotational velocity outside the VCL are shown to be influenced by the current-voltage relationship of the cathode and applied magnetic field strength. A basic characterization of the device and plasma environment is presented with an emphasis on diagnostics systems and the analytical techniques utilized.

Exploring the stellar rotation of early-type stars in the LAMOST medium-resolution survey

Context. Stellar rotation significantly shapes the evolution of massive stars, yet the interplay of mass and metallicity remains elusive, limiting our capacity to construct accurate stellar evolution models and to better estimate the impact of rotation on the chemical evolution of galaxies. Aims. Our goal is to investigate how mass and metallicity influence the rotational evolution of A-type stars on the main sequence (MS). We seek to identify deviations in rotational behaviors that could serve as new constraints for existing stellar models. Methods. Using the LAMOST Median-Resolution Survey Data Release 9, we derived stellar parameters for a population of 104 752 A-type stars. Our study focused on the evolution of surface rotational velocities and their dependence on mass and metallicity in 84 683 “normal” stars. Results. Normalizing surface rotational velocities to zero age main sequence (ZAMS) values revealed a prevailing evolutionary profile from 1.7 to 4.0 M⊙. This profile features an initial rapid acceleration until t/tMS = 0.25 ± 0.1 and potentially a second acceleration peak near t/tMS = 0.55 ± 0.1 for stars heavier than 2.5 M⊙, followed by a steady decline and a “hook” feature at the end. Surpassing theoretical expectations, the initial acceleration likely stems from a concentrated distribution of angular momentum at the ZAMS, resulting in a prolonged increase in speed. A transition phase for stars with 2.0 < M/M⊙ < 2.3 emerged, a region where evolutionary tracks remain uncertain. Stellar expansion primarily drives the spin down in the latter half of the MS, accompanied by significant influence from inverse meridional circulation. The inverse circulation becomes more efficient at lower metallicities, explaining the correlation of the slope of this deceleration phase with metallicity from –0.3 dex up to 0.1 dex. The metal-poor subsample (−0.3 dex < [M/H]< − 0.1 dex) starts with lower velocities at the ZAMS, suggesting that there is a metallicity-dependent mechanism that removes angular momentum during star formation. The proportion of fast rotators decreases with an increase in metallicity, up to log(Z/Z⊙)∼ − 0.2, a trend consistent with observations of OB-type stars found in the Small and Large Magellanic Clouds.

SPARC x-ray diagnostics: Technical and functional overview.

An overview is given of SPARC's three main x-ray diagnostics, with a focus on the functions they fulfill with respect to tokamak operation. The first is an in-vessel soft x-ray tomography diagnostic, aimed at providing early campaign information on plasma position, MHD activity, and impurity content. The second is an ex-vessel set of hard x-ray scintillators aimed at detecting the presence of runaway electrons, in particular during plasma startup phases. The third is a set of x-ray Bragg spectrometers, located outside of the tokamak hall, aimed at informing on the ion temperature as an indirect constraint to reduce uncertainties on the fusion power, on providing plasma rotation velocity estimates, and on observing impurity emission. Finally, more technical details are given on the beamlines at the end of which the spectrometers are located. It explains how their design allows us to ensure tritium containment and limit neutron radiation while providing a straight view into the plasma that can also be used for testing new innovative sensors.

The correlation between ball velocity with hip-shoulder rotation and separation during pitching process in baseball pitchers

<p>目的：本研究欲探討成棒選手肩髖的旋轉及肩髖分離程度與球速間的相關性，用以尋找提升球速的方法。方法：以 18 位大專公開一級棒球投手作為研究參與者，同時利用慣性感測 (IMU)、二維影像分析系統及測速槍測量研究參與者之投球運動學參數，包括肩與骨盆在各時間點的旋轉角度、肩髖分離的角度、旋轉峰值時機及球速等。以皮爾森積差相關係數分析肩與骨盆的旋轉情況及肩髖分離程度與球速之間是否具有相關性。結果：本研究顯示除了上軀幹在膝蓋最高點 (r =-.295, p =.441)外，其餘分別為上軀幹在前導腳落地時 (r = -.821, p < .001)、上軀幹在球離手時 (r = .765, p = .016)、骨盆在膝蓋最高點時 (r = -.791, p = .011)、骨盆在前導腳落地時 (r = .906, p= .001)、骨盆在球離手時 (r = .951, p < .001)，都與球速呈顯著相關；上軀幹與骨盆的旋轉速度峰值、時機與球速呈顯著相關 (r = .934, p < .001)、(r = .969, p < .001)、(r = .881, p = .002)、(r = -.749, p = .02)；肩髖分離程度與上軀幹和骨盆的旋轉及球速皆呈顯著相關。結論：本研究顯示不僅是上軀幹，骨盆的旋轉與球速也息息相關，因此在投球動作上應注重投球動作的整體性，而非強調單一肢段的發力，且若能同時妥善運用肩髖分離，則能提升運動表現。</p> <p> </p><p>Purpose: This study aims to investigate the correlation between hip-shoulder and separation degree with ball speed in skilled baseball pitchers to identify methods for enhancing pitching velocity. Methods: Eighteen collegiate level-Ⅰbaseball pitchers participated as research subjects. An inertial measurement unit (IMU), a two-dimensional motion analysis system, and a radar gun were employed to measure the kinematic parameters of the pitching motion. These parameters included rotational angles of the shoulder and pelvic at various time points, the degree of hip-shoulder separation, peak rotation timing, and ball velocity. Pearson correlation coefficients between ball velocity, hip shoulder separation, and all trunk and pelvic kinematic variables were computed, and the level of significance was set at α = .05. Results: The results indicate that, except for the upper trunk at the maximum knee height(r = -.295, p = .441), the rest were significantly related with ball velocity: the upper trunk at the landing of the leading foot (r = -.821, p< .001), the upper trunk at the ball off hand (r = .765, p = .016), the pelvic at the maximum knee height (r = -.791, p = .011), the pelvic at the landing of the leading foot (r = .906, p = .001), and the pelvic at the ball off hand (r = .951, p < .001). The peak rotation velocity and the timing of the peak rotation velocity of the upper trunk and pelvic is also significantly related to ball velocity(r = .934, p < .001)、(r = .969, p < .001)、(r = .881, p = .002)、(r = -.749, p = .02). The degree of shoulder-hip separation is significantly correlated with the rotation of the upper trunk and pelvic and ball velocity. Conclusion: Based on the findings of this study, we know the significance of not only the upper trunk but also pelvic rotation with ball velocity. Therefore, a holistic approach to pitching mechanics, emphasizing overall motion rather than isolating individual segments, is crucial. Additionally, effectively utilizing hip-shoulder separation can enhance overall athletic performance in baseball pitching.</p> <p> </p>

The Kraft Break Sharply Divides Low-mass and Intermediate-mass Stars

Main-sequence stars transition at mid-F spectral types from slowly rotating (cooler stars) to rapidly rotating (hotter stars), a transition known as the Kraft Break and attributed to the disappearance of the outer convective envelope, causing magnetic braking to become ineffective. To define this Break more precisely, we assembled spectroscopic measurements of 405 F stars within 33.33 pc. Once young, evolved, and candidate binary stars are removed, the distribution of projected rotational velocities shows the Break to be well defined and relatively sharp. Nearly all stars redder than G BP − G RP = 0.60 mag are slowly rotating (vsini ≲20 km s−1), while only 4 of 32 stars bluer than G BP − G RP = 0.54 mag are slowly rotating, consistent with that expected for a random distribution of inclinations. The Break is centered at an effective temperature of 6550 K and has a width of about 200 K, corresponding to a mass range of 1.32–1.41 M ⊙. The Break is ∼450 K hotter than the stellar temperature at which hot Jupiters show a change in their obliquity distribution, often attributed to tidal realignment. The Break, as defined above, is nearly but not fully established in the ∼650 Myr Hyades cluster; it should be established in populations older than 1 Gyr. We propose that the Kraft Break provides a more useful division, for both professional and pedagogical purposes, between what are called low-mass stars and intermediate-mass stars; the Kraft Break is observationally well defined and is linked to a change in stellar structure.

ISHELL K-band Survey of Class I and Flat Spectrum Sources: Magnetic Field Measurements in the Protostellar Phase

We perform the first magnetic field strength survey of Class I and Flat Spectrum (FS) sources using K-band observations with iSHELL. We obtained new observations of 42 Class I and FS sources and additionally included 10 sources from the archive. We detect photospheric lines in 44 of the sources, in addition to Brγ, H2, and CO emission in several objects. We model the photospheric absorption lines of 32 Class I and FS sources and measure their magnetic field strengths, K-band temperatures, gravities, projected rotational velocities, and infrared veiling values. We put the physical properties of Class I and FS sources in context by comparing them to the values derived for a sample of Class II sources. We find that (a) the average magnetic field strength of Class I and FS sources 〈B〉 = 2.0 ± 0.15 kG is consistent with the average magnetic field strength of Class II sources 〈B〉 = 1.8 ± 0.15 kG, and (b) the average gravity of Class I and FS objects logg=3.43±0.07 is lower than the average gravity of Class II sources logg=3.75±0.04 , although there is significant overlap between both gravity distributions. Furthermore, using stellar evolutionary models, we deduce that Class I and FS sources have a median age of ∼0.6 Myr, and are, as a group, younger than the Class II stars with a median age of ∼3 Myr. Our results confirm that Class I and FS sources host strong magnetic fields on their photospheres. Thus, it is likely that these sources accrete disk material through a magnetosphere similar to the more evolved T Tauri stars.

From gas to stars: MUSEings on the internal evolution of IC 1613

Context. The kinematics and chemical composition of stellar populations of different ages provide crucial information on the evolution of the various components of a galaxy. Aim. Our aim is to determine the kinematics of individual stars as a function of age in IC 1613, a star-forming, gas-rich, and isolated dwarf galaxy of the Local Group (LG). Methods. We present results of a new spectroscopic survey of IC 1613 conducted with MUSE, an integral field spectrograph mounted on the Very Large Telescope. We extracted ∼2000 sources, from which we separated stellar objects for their subsequent spectral analysis. The quality of the dataset allowed us to obtain accurate classifications (Teff to better than 500 K) and line-of-sight velocities (with average δv ∼ 7 km s−1) for about 800 stars. Our sample includes not only red giant branch (RGB) and main sequence (MS) stars, but also a number of probable Be and C stars. We also obtained reliable metallicities (δ[Fe/H] ∼ 0.25 dex) for about 300 RGB stars. Results. The kinematic analysis of IC 1613 revealed for the first time the presence of stellar rotation with high significance. We found general agreement with the rotation velocity of the neutral gas component. Examining the kinematics of stars as a function of broad age ranges, we find that the velocity dispersion increases as a function of age, with the behaviour being very clear in the outermost pointings, while the rotation-to-velocity dispersion support decreases. On timescales of < 1 Gyr, the stellar kinematics still follow very closely that of the neutral gas, while the two components decouple on longer timescales. The chemical analysis of the RGB stars revealed average properties comparable to other Local Group dwarf galaxies. We also provide a new estimation of the inclination angle using only independent stellar tracers. Conclusions. Our work provides the largest spectroscopic sample of an isolated LG dwarf galaxy. The results obtained seem to support the scenario in which the stars of a dwarf galaxy are born from a less turbulent gas over time.

Literature review of specific techniques in catching and throwing in infield defense in baseball - retrospective article

<p>目的：內野手可以是整個棒球守備的核心，棒球守備各階段全身上下的協調，有許多值得探討的專項技巧。方法：本研究使用Google scholar，以Baseball infielder、內野、野球守備、內野捕球、守備ゴロ等關鍵字，搜尋台灣、日本、美國三國關於棒球內野守備專項技巧的文獻做歸納，以不同角度探討內野守備的專項技巧：一、內野守備接球，二、內野守備傳球，三、守備的分期與各分期之動作控制。結果：本篇回顧性論文發現，一、移動腳步到好接球的彈跳點是良好守備的關鍵。二、減少軸心腳在接球位置上的變化和較為前面的接球點，對於接球的穩定性至關重要，甚至會影響到後續傳球的動能。三、精簡接傳的動作相較於增加傳球球速可能可以更能有效減少整體守備時間。四、優秀選手在接球的過程中會儘早讓軸心腳著地，並前期和中期將重心保留在軸心腳。五、內野手傳球在前導腳接觸時，軀幹向後扭轉和肘部伸展角度都會比投手小。結論：無論是接球前腳步移動的節奏和精確性，還是接球時的接球點和接短彈跳的能力，甚至是軀幹和骨盆前傾的時機點，對於內野守備過程都產生一定的影響。建議在日常練習時，就能將接短彈跳、腳步移動，納入訓練課表中，並且在動作過程中，加以檢視軀幹的姿勢，方能在比賽時擁有良好的守備表現。</p> <p> </p><p>The standing throw with run-up is the best approach to evaluate the performance of energy transfer and the efficiency of throwing motions for handball players. Purpose: This research aims at analyzing the usage of the standing throw with run-up among the handball players in Taiwan. The roles of body kinematics, strength of core muscles and standing balance of the drive leg played in the standing throw with run-up are also discussed. Methods: Nine Division I handball players from college went through a series of tests. The motions and the speed of the handball throwing were detected by a 3D electromagnetic motion analysis system and a sports radar gun, respectively. The maximum isometric muscle strength of trunks and hips were measured by a torque sensor and a home-made device of strength measurement. The standing balance of the drive leg was measured by a force plate with a mat. Results: The maximal shoulder external rotation angle in the arm cocking phase, the maximal trunk rotation velocity in the arm acceleration phase and the maximal shoulder horizontal adduction velocity showed moderate positive relationships with the ball velocity. The strength of back muscles had a moderate negative relationship with the ball velocity. The correlation between the balance ability of the drive leg and the ball velocity was not observed. Conclusion: The importance of proximal segments to the standing throw with run-up is analyzed by kinematical analysis. It is suggested that the energy of handball throwing is generated by the upper extremities or other limb segments in the processes of the standing throw with run-up. Our findings can serve as a helpful reference for both coaches and players.</p> <p> </p>

Field equation of thermodynamic gravity and galactic rotational curves

The rotational velocity curve (RC) of galaxy NGC 3198 is modelled in various theoretical frameworks: Thermodynamic Gravity (TG) is compared to Dark Matter (DM) and Modified Newtonian Dynamics (MOND). The nonlinear gravitational field equation of TG is solved using the baryonic mass density as the source of the gravitational field. In this paper, first, a dissipation motivated numerical method is verified with the help of exact solutions. Then, the obtained optimal velocity curve is compared to DC14 model DM and MOND EFE (Modified Newtonian Dynamics-External Field Effect aspect) parametrisations for the RC of the galaxy.

Sulfur monoxide (SO) as a shock tracer in protoplanetary disks: Case of AB Aurigae

Context. Sulfur monoxide (SO) is known to be a good shock tracer in molecular clouds and protostar environments, but its abundance is difficult to reproduce, even with state-of-the-art astrochemical models. Aims. We investigate the properties of the observed SO emission in the protoplanetary disk of AB Auriga, a Herbig Ae star of 2.4 M⊙ in mass, located at 156 pc. The AB Aur system is unique because it exhibits a dust trap and at least one young putative planet orbiting at about 30 au from the central star. Methods. We reduced ALMA archival data (projects 2019.1.00579.S, 2021.1.00690.S, and 2021.1.01216.S) and analyzed the three detected SO lines (SO 65 − 54, 67 − 56 and 56 − 45). We also used C17O and C18O 2–1 data to complement the interpretation of the SO data. Results. For the three SO lines, the maximum SO emission in the ring is not located in the dust trap. Moreover, the inner radius of the SO ring is significantly larger than the CO emission inner radius, ∼160 au versus ∼90 au. The SO emission traces gas located in part beyond the dust ring. This emission likely originates from shocks at the interface of the outer spirals, observed in CO and scattered light emission, as well as those in the molecular and dust ring. Also, SO is detected within the cavity, at a radius of ∼20 − 30 au and with a rotation velocity compatible with the protoplanet P1. We speculate that this SO emission originates from accretion shocks onto the circumplanetary disk of the putative protoplanet P1. Conclusions. These observations confirm that SO is a good tracer of shocks in protoplanetary disks and could serve as a powerful new tool for detecting embedded (proto)planets.

Orbital angular momentum and rotational properties of off-axis vortex beams in two-dimensional media with anisotropic nonlocal nonlinearity.

By introducing anisotropy into nonlinear propagations, off-axis vortex beams exhibit significantly different characteristics compared to the isotropic case. The orbital angular momentum (OAM) is non-conservative and can periodically change between positive and negative values. Accordingly, the rotation of phase singularity can transit between clockwise and counterclockwise directions. Furthermore, the phase singularity can move to infinity when the OAM approaches zero. By using the Ehrenfest theorem, the motion of the beam center is obtained. Its trajectory can be circular and parabolic or follow other complex shapes, depending closely on the anisotropy of the nonlinearity. The rotational velocity of the beam center can be modulated by the nonlinearity anisotropy and can far exceed the initial value during its propagation. These results may find potential applications in beam shaping and optical manipulation.

Hierarchical attitude stabilization controller design and analysis for underactuated spacecraft on SO(3)

In this paper, the complete attitude stabilization of underactuated spacecraft with two parallel single gimbal control moment gyroscopes (SGCMGs) is explored on 3-dimensional special orthogonal group (SO(3)) and its corresponding Lie algebra (so(3)). Instead of assumption on zero total angular momentum in existing article, a less conservative criterion is adopted to ensure system controllability, which does not simplify system dynamics. On the kinematic level, an ideal controller is proposed to globally stabilize attitude without singular initial condition and stagnation behavior. Besides, the ideal kinematic controller is developed on so(3), which avoids singularity or unwinding phenomenon caused by other attitude parameters. On the dynamic level, a hierarchical controller consisting of two parts is proposed. The high-level sliding mode part enforces finite time stabilization of angular velocity about underactuated axis while the low-level part tracks ideal angular velocity commands about actuated axes. A rigorous proof of the whole dynamic-kinematic system that has not been explored before is given. Analysis of hierarchical control from the perspective of linear algebra provides a novel insight into controller design for underactuated systems. Furthermore, the paradigm of controller design which is applicable to other underactuated systems is derived. Simulation results validate the effectiveness of the proposed control logic.