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Inertia

About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.


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Journal ArticleDOI
TL;DR: Gravity exerted a greater influence than inertia on both vertical and horizontal forces generated against the ground during running, and maintaining the orientation of the resultant vector during periods of high force generation aligns the vector with the leg to minimize muscle forces.
Abstract: It is difficult to distinguish the independent effects of gravity from those of inertia on a running animal. Simply adding mass proportionally changes both the weight (gravitational force) and mass (inertial force) of the animal. We measured ground reaction forces for eight male humans running normally at 3 m s -1 and under three experimental treatments: added gravitational and inertial forces, added inertial forces and reduced gravitational forces. Subjects ran at 110, 120 and 130 % of normal weight and mass, at 110, 120 and 130 % of normal mass while maintaining 100 % normal weight, and at 25, 50 and 75 % of normal weight while maintaining 100 % normal mass. The peak active vertical forces generated changed with weight, but did not change with mass. Surprisingly, horizontal impulses changed substantially more with weight than with mass. Gravity exerted a greater influence than inertia on both vertical and horizontal forces generated against the ground during running. Subjects changed vertical and horizontal forces proportionately at corresponding times in the step cycle to maintain the orientation of the resultant vector despite a nearly threefold change in magnitude across treatments. Maintaining the orientation of the resultant vector during periods of high force generation aligns the vector with the leg to minimize muscle forces. Summary

125 citations

Journal ArticleDOI
TL;DR: In this paper, a mean-field analysis of a Kuramoto model with inertia was performed for fully coupled and diluted systems, and it was shown that the transition from incoherence to coherence is hysteretic.
Abstract: We report finite-size numerical investigations and mean-field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine, for a gaussian distribution of the frequencies, the transition from incoherence to coherence for increasingly large system size and inertia. For sufficiently large inertia the transition is hysteretic, and within the hysteretic region clusters of locked oscillators of various sizes and different levels of synchronization coexist. A modification of the mean-field theory developed by Tanaka, Lichtenberg, and Oishi [Physica D 100, 279 (1997)] allows us to derive the synchronization curve associated to each of these clusters. We have also investigated numerically the limits of existence of the coherent and of the incoherent solutions. The minimal coupling required to observe the coherent state is largely independent of the system size, and it saturates to a constant value already for moderately large inertia values. The incoherent state is observable up to a critical coupling whose value saturates for large inertia and for finite system sizes, while in the thermodinamic limit this critical value diverges proportionally to the mass. By increasing the inertia the transition becomes more complex, and the synchronization occurs via the emergence of clusters of whirling oscillators. The presence of these groups of coherently drifting oscillators induces oscillations in the order parameter. We have shown that the transition remains hysteretic even for randomly diluted networks up to a level of connectivity corresponding to a few links per oscillator. Finally, an application to the Italian high-voltage power grid is reported, which reveals the emergence of quasiperiodic oscillations in the order parameter due to the simultaneous presence of many competing whirling clusters.

124 citations

Journal ArticleDOI
TL;DR: In this paper, a modified Reynolds equation where the gas inertia effect is included from the Navier-Stokes equation is derived, and the model response is compared with 2D and 3D FEM time-domain and frequency-domain simulations with excellent agreement.
Abstract: A modified Reynolds equation where the gas inertia effect is included is derived from the Navier–Stokes equation. Continuum and slip-flow regions are modelled. Small flow velocity is assumed, and border effects are not considered. By introducing an effective flow rate coefficient including the inertial and rare gas effects, existing linearized analytic squeezed-film damping models can be reused. Equivalent-circuit mechanical impedance and admittance implementations for a rectangular parallel-plate damper are given. The model response is compared against 2D and 3D FEM time-domain and frequency-domain simulations with an excellent agreement. The validity and limitations of the models are discussed extensively.

124 citations

Proceedings ArticleDOI
10 Apr 2007
TL;DR: The reaction mass pendulum (RMP) model is introduced, a 3D generalization of the better-known reaction wheel pendulum, which provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws.
Abstract: A number of conceptually simple but behavior-rich "inverted pendulum" humanoid models have greatly enhanced the understanding and analytical insight of humanoid dynamics. However, these models do not incorporate the robot's angular momentum properties, a critical component of its dynamics. We introduce the reaction mass pendulum (RMP) model, a 3D generalization of the better-known reaction wheel pendulum. The RMP model augments the existing models by compactly capturing the robot's centroidal momenta through its composite rigid body (CRB) inertia. This model provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws. In this paper we show how a humanoid robot of general geometry and dynamics can be mapped into its equivalent RMP model. A movement is subsequently mapped to the time evolution of the RMP. We also show how an "inertia shaping" control law can be designed based on the RMP.

124 citations

Journal ArticleDOI
TL;DR: In this article, a spatial distribution of singular torques, called rotlets, by which the rotational motion of a given body can be represented is explored, and exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms.
Abstract: The present series of studies is concerned with low-Reynolds-number flow in general; the main objective is to develop an effective method of solution for arbitrary body shapes. In this first part, consideration is given to the viscous flow generated by pure rotation of an axisymmetric body having an arbitrary prolate form, the inertia forces being assumed to have a negligible effect on the flow. The method of solution explored here is based on a spatial distribution of singular torques, called rotlets, by which the rotational motion of a given body can be represented. Exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms. In the special case of prolate spheroids, the present exact solution agrees with that of Jeffery (1922), this being one of very few cases where previous exact solutions are available for comparison. The velocity field and the total torque are derived, and their salient features discussed for several representative and limiting cases. The moment coefficient C[sub]M = M/(8[pi][mu][omega sub 0]ab^2) (M being the torque of an axisymmetric body of length 2a and maximum radius b rotating at angular velocity [omega], about its axis in a fluid of viscosity [mu]) of various body shapes so far investigated is found to lie between 2/3 and 1, usually very near unity for not extremely slender bodies. For slender bodies, an asymptotic relationship is found between the nose curvature and the rotlet strength near the end of its axial distribution. It is also found that the theory, when applied to slender bodies, remains valid at higher Reynolds numbers than was originally intended, so long as they are small compared with the (large) aspect ratio of the body, before the inertia effects become significant.

124 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023886
20221,975
2021443
2020562
2019609
2018566