This paper introduces a simplified matrix method for balancing forces and moments in planar parallel manipulators. The method resorts to Newton’s second law and the concept of angular momentum vector, yet it is not necessary to perform the velocity and acceleration analyses, tasks that were normally unavoidable in seminal contributions. With the introduction of natural matrices, the proposed balancing method is independent of the time and the trajectory generated by the moving links of parallel manipulators. The effectiveness of the method is exemplified by balancing two planar parallel manipulators.

Magnetic fields are a key component in star formation theories. Nevertheless, their exact role in the formation of stars is still a matter of debate. The process of angular momentum transportation by the disturbance caused during magnetic field reconnection still needs theoretical formulation in terms of the collapsing cloud’s parameters. The purposes of this study are: to model the critical mass of a magnetized, gravitating and turbulent star forming molecular cloud (MC) and to formulate the momentum carried out by a magnetic field through magnetic field reconnection in terms of the MC’s parameters. By applying theoretical modeling, we show how angular momentum transported via an Alfvén wave can be described in terms of mass, radius and dispersion velocity of a collapsing cloud core and a model equation of the critical mass for a gravitating, turbulent, and magnetized molecular cloud core. The outflow of angular momentum by magnetic fields facilitates the inflow of mass. On the other side, magnetic pressure prevents collapse. Therefore, magnetic fields have a dual purpose in the process of star formation. This momentum outflow triggers the inflow of mass to conserve angular momentum. The results show that Alfvén waves are like a machine that extracts angular momentum from a magnetized collapsing cloud core. Thus the total angular momentum transported by magnetic field at a distance R from the core’s center depends on the size, mass and turbulent velocity dispersion of the collapsing cloud core.

Throughout the Hubble time, gas makes its way from the intergalactic medium into galaxies fuelling their star formation and promoting their growth. One of the key properties of the accreting gas is its angular momentum, which has profound implications for the evolution of, in particular, disc galaxies. Here, we discuss how to infer the angular momentum of the accreting gas using observations of present-day galaxy discs. We first summarize evidence for ongoing inside-out growth of star forming discs. We then focus on the chemistry of the discs and show how the observed metallicity gradients can be explained if gas accretes onto a disc rotating with a velocity 20 – 30% lower than the local circular speed. We also show that these gradients are incompatible with accretion occurring at the edge of the discs and flowing radially inward. Finally, we investigate gas accretion from a hot corona with a cosmological angular momentum distribution and describe how simple models of rotating coronae guarantee the inside-out growth of disc galaxies.

Recent measurements of the chemical and isotopic composition of lunar samples indicate that the Moon's bulk composition shows great similarities with the composition of the silicate Earth. Moon formation models that attempt to explain these similarities make a wide variety of assumptions about the properties of the Earth prior to the formation of the Moon (the proto-Earth), and about the necessity and properties of an impactor colliding with the proto-Earth. This paper investigates the effects of the proto-Earth's mass, oblateness and internal core-mantle differentiation on its moment of inertia. The ratio of angular momentum and moment of inertia determines the stability of the proto-Earth and the binding energy, i.e. the energy needed to make the transition from an initial state in which the system is a rotating single body with a certain angular momentum to a final state with two bodies (Earth and Moon) with the same total angular momentum, redistributed between Earth and Moon. For the initial state two scenarios are being investigated: a homogeneous (undifferentiated) proto-Earth and a proto-Earth differentiated in a central metallic and an outer silicate shell; for both scenarios a range of oblateness values is investigated. Calculations indicate that a differentiated proto-Earth would become unstable at an angular momentum L that exceeds the total angular momentum of the present-day Earth–Moon system (L0) by factors of 2.5–2.9, with the precise maximum dependent on the proto-Earth's oblateness. Further limitations are imposed by the Roche limit and the logical condition that the separated Earth–Moon system should be formed outside the proto-Earth. This further limits the L values of the Earth–Moon system to a maximum of about L/L0 = 1.5, at a minimum oblateness (a/c ratio) of 1.2. These calculations provide boundary conditions for the main classes of Moon-forming models. Our results show that at the high values of L used in recent giant impact models (1.8 < L/L0 < 3.1), the proposed proto-Earths are unstable before (Cuk & Stewart, 2012) or immediately after (Canup, 2012) the impact, even at a high oblateness (the most favourable condition for stability). We conclude that the recent attempts to improve the classic giant impact hypothesis by studying systems with very high values of L are not supported by the boundary condition calculations in this work. In contrast, this work indicates that the nuclear explosion model for Moon formation (De Meijer et al., 2013) fulfills the boundary conditions and requires approximately one order of magnitude less energy than originally estimated. Hence in our view the nuclear explosion model is presently the model that best explains the formation of the Moon from predominantly terrestrial silicate material.

This paper presents the preimpact configuration of a dual-arm space manipulator with a prismatic joint for capturing an object based on the momentum conservation principle. A unique precapture configuration “generalized straight-arm capture” (GSAC) is proposed based on the dual-arm space manipulator with a prismatic joint and the corresponding angular relation is obtained. The configuration satisfies GSAC and can reduce the effect of system's angular momentum caused by the impact force during the capture operation and the burden of postimpact control, so it avoids the limitation of joint velocity and actuator torque when controlling the compound (a manipulator with a prismatic joint and an object) and guarantees the stability of the system. Finally, the effectiveness of the method is demonstrated by numerical simulations.

The orbital angular momenta OAM (J) of detached binaries (including both cool and hot binaries) were estimated and nine subgroups were formed according to their OAM (J) distribution. The mean kinematical ages of all subgroups have been estimated by using their space velocity distributions and, thus, the age dependent variations of the mean OAM (J), orbital period (P), and total mass (M) of all subgroups were investigated. It was discovered that: i) The orbital period of detached binaries with radiative components decrease very slowly during the main sequence (MS) evolution. It is interesting that the large amount of mass loss is almost balanced by the OAM loss, and not much change in the orbital periods is observed. ii) The nuclear evolution of radiative components beyond the MS initiates the increase of the periods until the components have convective upper layers, i.e. until they become later than F5 IV, and the system becomes a cool binary with sub-giant or giant components. iii) The large co-rotating distance of the magnetically-driven wind in cool binaries (CAB) carries out a large amount of OAM and then the periods of such binaries decrease significantly, and the orbits shrink until another effect such as mass transfer dominates the period changes.

A real-time joint trajectory generator for planar walking bipeds is proposed. This trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the developed strategy is demonstrated by simulation results.