Change Of Linear Momentum Research Articles

Whole-body momentum control with linear quadratic state incremental walking pattern generation and a centroidal moment pivot balancing strategy for humanoid robots

ABSTRACT In this paper, a proposed momentum control framework adopts the quadratic programming method to handle the multi-task prioritized problem by assigning suitable constraints and the objective function, including desired end-effectors motions, the limitations of joints and the rate of change of linear and angular momentum of a robot. First, the centroidal momentum matrix is used to derive the relationship between the linear and angular momentum of the center of mass and the whole-body motion of the robot. Second, the linear quadratic state incremental walking pattern generator is used to regulate the rate of change of linear momentum of the robot for balanced walking. Then, according to the difference between the centroidal moment pivot and the zero moment point (ZMP), the compensatory rate of change of horizontal angular momentum can be calculated to keep the balance from unexpected larger disturbances. Finally, the performance of this control framework is verified effectively through the simulations and the experiments. In addition, the ZMP tracking performance is improved up to 50% in the simulations and 14% in the experiments.

Conservative and radiative dynamics in classical relativistic scattering and bound systems

As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the post-Minkowskian approach to the gravitational two-body problem, where the field has only recently reached a full description of certain physical observables for scattering orbits, including radiative effects, at the third post-Minkowskian (3PM) order. As an historically instructive simpler example, we consider here the analogous problem in electromagnetism in flat spacetime. We compute the changes in linear momentum of each particle and the total radiated linear momentum, in the relativistic classical scattering of two point-charges, at sixth order in the charges (analogous to 3PM order in gravity). We accomplish this here via direct iteration of the classical equations of motion, while making comparisons where possible to results from quantum scattering amplitudes, with the aim of contributing to the elucidation of conceptual issues and scalability on both sides. We also discuss further extensions to radiative quantities of recently established relations, which analytically continue certain observables from the scattering regime to the regime of bound orbits, applicable for both the electromagnetic and gravitational cases.

A Numerical Analysis of Bidirectional Ducted Tidal Turbines in Yawed Flow

AbstractThe paper presents a computational study of ducted bidirectional tidal turbines using three-dimensional Reynolds-averaged Navier-Stokes simulations. We model the outer duct as a solid body and use a porous disc to represent the turbine rotor, a simplification that captures changes in linear momentum and thus the primary interaction of the turbine with the flow through and around the duct while greatly reducing computational complexity. The duct is modeled using linearly converging and diverging sections and a short straight pipe at the duct throat.We investigate the performance of bare and ducted turbines and relate these to the flows through the devices. For the ducted turbine under investigation, we show a substantial decrease in power generated relative to a bare turbine of diameter equal to the external diameter of the duct. In the case of ducted turbines with concave duct exteriors, we observe two external flow regimes with increasing turbine thrust: nozzle-contoured and separation dominated regimes. Maximum power occurs within the separation dominated flow regime due to the additional channel blockage created by the external separation.The ducts of ducted tidal turbines have been argued to provide a flow straightening effect, allowing modest yaw angles to be readily accommodated. We present a comparison of bare and ducted turbine performance in yawed flow. We show that while bare turbine performance decreases in yawed flow, ducted turbine performance increases. This is due to both a flow straightening effect and also an increase in effective blockage as ducts present greater projected frontal area when approached nonaxially.