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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: A microscopic ordinary differential equation (ODE)-based model for pedestrian dynamics: the gradient navigation model, which uses a superposition of gradients of distance functions to directly change the direction of the velocity vector and which introduces a method to calibrate parameters by theoretical arguments based on empirical assumptions rather than by numerical tests.
Abstract: We present a microscopic ordinary differential equation (ODE)-based model for pedestrian dynamics: the gradient navigation model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is then integrated to obtain the location. The approach differs fundamentally from force-based models needing only three equations to derive the ODE system, as opposed to four in, e.g., the social force model. Also, as a result, pedestrians are no longer subject to inertia. Several other advantages ensue: Model-induced oscillations are avoided completely since no actual forces are present. The derivatives in the equations of motion are smooth and therefore allow the use of fast and accurate high-order numerical integrators. At the same time, the existence and uniqueness of the solution to the ODE system follow almost directly from the smoothness properties. In addition, we introduce a method to calibrate parameters by theoretical arguments based on empirically validated assumptions rather than by numerical tests. These parameters, combined with the accurate integration, yield simulation results with no collisions of pedestrians. Several empirically observed system phenomena emerge without the need to recalibrate the parameter set for each scenario: obstacle avoidance, lane formation, stop-and-go waves, and congestion at bottlenecks. The density evolution in the latter is shown to be quantitatively close to controlled experiments. Likewise, we observe a dependence of the crowd velocity on the local density that compares well with benchmark fundamental diagrams.

78 citations

Journal ArticleDOI
TL;DR: In this paper, the authors compare and evaluate existing complete balancing principles regarding the addition of mass and inertia and introduce a normalized indicator to judge the balancing performance regarding the added mass and the inertia.
Abstract: The major disadvantage of existing dynamic balancing principles is that a considerable amount of mass and inertia is added to the system The objectives of this article are to summarize, to compare, and to evaluate existing complete balancing principles regarding the addition of mass and the addition of inertia and to introduce a normalized indicator to judge the balancing performance regarding the addition of mass and inertia The balancing principles are obtained from a survey of literature and applied to a double pendulum for comparison, both analytically and numerically The results show that the duplicate mechanisms principle has the least addition of mass and also a low addition of inertia and is most advantageous for low-mass and low-inertia dynamic balancing if available space is not a limiting factor Applying countermasses and separate counter-rotations with or without an idler loop both increase the mass and inertia considerably, with idler loop being the better of the two Using the force-balancing countermasses also as moment-balancing counterinertias leads to significantly less mass addition as compared with the use of separate counter-rotations For low transmission ratios, also the addition of inertia then is smaller

78 citations

Journal ArticleDOI
TL;DR: In this article, the authors apply the energy-momentum method to the stability analysis of uniformly rotating states of geometrically exact rod models, and a rigid body with an attached flexible appendage.

78 citations

Journal ArticleDOI
TL;DR: This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates, thus making it suitable for control design.
Abstract: A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

78 citations

Proceedings Article
01 Feb 1991

77 citations


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