scholarly journals Constraint rescaling in refined algebraic quantisation: Momentum constraint

2011 ◽  
Vol 52 (12) ◽  
pp. 123504 ◽  
Author(s):  
Jorma Louko ◽  
Eric Martínez-Pascual
Keyword(s):  
Momentum Constraint

scholarly journals Momentum constraint relaxation

2006 ◽  
Vol 23 (7) ◽  
pp. 2681-2695 ◽  
Author(s):  
Pedro Marronetti
Keyword(s):  
Constraint Relaxation ◽  
Momentum Constraint

YAW MOMENT COMPENSATION FOR BIPEDAL ROBOTS VIA INTRINSIC ANGULAR MOMENTUM CONSTRAINT

2012 ◽  
Vol 09 (04) ◽  
pp. 1250033 ◽  
Author(s):  
BARKAN UGURLU ◽  
JODY A. SAGLIA ◽  
NIKOS G. TSAGARAKIS ◽  
DARWIN G. CALDWELL
Keyword(s):  
Angular Momentum ◽  
Bipedal Walking ◽  
Upper Body ◽  
Rotational Inertia ◽  
Bipedal Robots ◽  
Bipedal Robot ◽  
Crucial Component ◽  
Intrinsic Angular Momentum ◽  
Momentum Constraint ◽  
Yaw Moment

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.

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

2004 ◽  
Vol 61 (23) ◽  
pp. 2899-2908 ◽  
Author(s):  
Theodore G. Shepherd ◽  
Tiffany A. Shaw
Keyword(s):  
Angular Momentum ◽  
Gravity Wave ◽  
Middle Atmosphere ◽  
Wave Drag ◽  
Planetary Waves ◽  
Source Spectrum ◽  
Strong Constraint ◽  
Wave Source ◽  
Downward Influence ◽  
Momentum Constraint

Abstract 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.

scholarly journals A generalized Momentum/Complexity correspondence

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
J. L. F. Barbón ◽  
J. Martín-García ◽  
M. Sasieta
Keyword(s):  
General Relativity ◽  
Wave Solution ◽  
Einstein Equations ◽  
Rate Of Growth ◽  
Starting Point ◽  
Vacuum Einstein Equations ◽  
Generalized Momentum ◽  
Pp Wave ◽  
Momentum Constraint ◽  
Codazzi Equations

Abstract 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.

Control of foot placement, forward velocity and body orientation of a one-legged hopping robot

Robotica ◽  
2003 ◽  
Vol 21 (1) ◽  
pp. 45-57 ◽  
Author(s):  
J. Vermeulen ◽  
D. Lefeber ◽  
B. Verrelst
Keyword(s):  
Angular Momentum ◽  
Control Algorithm ◽  
Stance Phase ◽  
Step Length ◽  
Center Of Gravity ◽  
Foot Placement ◽  
Irregular Terrain ◽  
Hopping Robot ◽  
Parabolic Trajectory ◽  
Momentum Constraint

This paper intends to contribute to the study of dynamically balanced legged robots. A real-time applicable control algorithm for a planar one-legged robot is developed, which allows for locomotion on an irregular terrain. The simulated model consists of an articulated leg and a body, vertically placed upon the leg. During the stance phase the leg is supported by a massless foot. The algorithm is based on the choice of a number of objective locomotion parameters which can be changed from one hop to another. From a chosen initial configuration the robot is able to transfer to a chosen end configuration, while simultaneously controlling its forward velocity, its step length and its stepping height. The foot is thus being placed exactly on a chosen foothold. To reach this goal, the actuators track polynomial functions. The calculation of these functions is based on the objective parameters, and takes into account the constraints acting on the robot. These constraints result from the fact that during flight the center of gravity of the robot tracks a parabolic trajectory, and that the angular momentum with respect to the center of gravity is conserved. Writing the angular momentum constraint in a Caplygin form is the key to the algorithm. Promising simulation results for the algorithm are shown for two different experiments.

scholarly journals Vertical angular momentum constraint on lunar formation and orbital history

2020 ◽  
Vol 117 (27) ◽  
pp. 15460-15464 ◽  
Author(s):  
ZhenLiang Tian ◽  
Jack Wisdom
Keyword(s):  
Angular Momentum ◽  
Orbital Plane ◽  
Orbital Evolution ◽  
The Moon ◽  
Moon System ◽  
Left Behind ◽  
System A ◽  
The Earth ◽  
Momentum Constraint ◽  
Fast Rotating

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.

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