A generalized Momentum/Complexity correspondence

Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity correspondence can be related to an integrated version of the momentum constraint of general relativity. In this paper we propose a generalization, using the full Codazzi equations as a starting point, which successfully accounts for purely gravitational contributions to infall momentum. The proposed formula is explicitly checked in an exact pp-wave solution of the vacuum Einstein equations.

Vertical angular momentum constraint on lunar formation and orbital history

The Moon likely formed in a giant impact that left behind a fast-rotating Earth, but the details are still uncertain. Here, we examine the implications of a constraint that has not been fully exploited: The component of the Earth–Moon system’s angular momentum that is perpendicular to the Earth’s orbital plane is nearly conserved in Earth–Moon history, except for possible intervals when the lunar orbit is in resonance with the Earth’s motion about the Sun. This condition sharply constrains the postimpact Earth orientation and the subsequent lunar orbital history. In particular, the scenario involving an initial high-obliquity Earth cannot produce the present Earth–Moon system. A low-obliquity postimpact Earth followed by the evection limit cycle in orbital evolution remains a possible pathway for producing the present angular momentum and observed lunar composition.

YAW MOMENT COMPENSATION FOR BIPEDAL ROBOTS VIA INTRINSIC ANGULAR MOMENTUM CONSTRAINT

This paper is aimed at describing a technique to compensate undesired yaw moment, which is inevitably induced about the support foot during single support phases while a bipedal robot is in motion. The main strategy in this method is to rotate the upper body in a way to exert a secondary moment that counteracts to the factors which create the undesired moment. In order to compute the yaw moment by considering all the factors, we utilized Eulerian ZMP Resolution, as it is capable of characterizing the robot's rotational inertia, a crucial component of its dynamics. In doing so, intrinsic angular momentum rate changes are smoothly included in yaw moment equations. Applying the proposed technique, we conducted several bipedal walking experiments using the actual bipedal robot CoMan. As the result, we obtained 61% decrease in undesired yaw moment and 82% regulation in yaw-axis deviation, which satisfactorily verify the efficiency of the proposed approach, in comparison to off-the-shelf techniques.

The Angular Momentum Constraint on Climate Sensitivity and Downward Influence in the Middle Atmosphere

It is shown that under reasonable assumptions, conservation of angular momentum provides a strong constraint on gravity wave drag feedbacks to radiative perturbations in the middle atmosphere. In the time mean, radiatively induced temperature perturbations above a given altitude z cannot induce changes in zonal mean wind and temperature below z through feedbacks in gravity wave drag alone (assuming an unchanged gravity wave source spectrum). Thus, despite the many uncertainties in the parameterization of gravity wave drag, the role of gravity wave drag in middle-atmosphere climate perturbations may be much more limited than its role in climate itself. This constraint limits the possibilities for downward influence from the mesosphere. In order for a gravity wave drag parameterization to respect the momentum constraint and avoid spurious downward influence, any nonzero parameterized momentum flux at a model lid must be deposited within the model domain, and there must be no zonal mean sponge layer. Examples are provided of how violation of these conditions leads to spurious downward influence. For planetary waves, the momentum constraint does not prohibit downward influence, but it limits the mechanisms by which it can occur: in the time mean, downward influence from a radiative perturbation can only arise through changes in reflection and meridional propagation properties of planetary waves.