Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 559-569 ◽  
Author(s):  
A. A. Barhorst ◽  
L. J. Everett
Keyword(s):  
Initial Conditions ◽  
System Modeling ◽  
Variational Calculus ◽  
Nonholonomic Constraints ◽  
Modeling Methodology ◽  
Starting Point ◽  
Holonomic And Nonholonomic Constraints ◽  
Contact Impact ◽  
Nature Of Time ◽  
Hybrid Differential Equations

The multiple motion regime (free/constrained) dynamics of hybrid parameter multiple body (HPMB) systems is addressed. Impact response has characteristically been analyzed using impulse-momentum techniques. Unfortunately, the classical methods for modeling complex HPMB systems are energy based and have proven ineffectual at modeling impact. The problems are exacerbated by the problematic nature of time varying constraint conditions. This paper outlines the reformulation of a recently developed HPMB system modeling methodology into an impulse-momentum formulation, which systematically handles the constraints and impact. The starting point for this reformulation is a variational calculus based methodology. The variational roots of the methodology allows rigorous equation formulation which includes the complete nonlinear hybrid differential equations and boundary conditions. Because the methodology presented in this paper is formulated in the constraint-free subspace of the configuration space, both holonomic and nonholonomic constraints are automatically satisfied. As a result, the constraint-addition/deletion algorithms are not needed. Generalized forces of constraint can be directly calculated via the methodology, so the condition for switching from one motion regime to another is readily determined. The resulting equations provides a means to determine after impact velocities (and velocity fields for distributed bodies) which provide the after collision initial conditions. Finally the paper demonstrates, via example, how to apply the methodology to contact/impact in robotic manipulators and structural systems.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

Obtaining the Minimal Set of Hybrid Parameter Differential Equations for Mechanisms

1992 ◽  
Author(s):  
Alan A. Barhorst ◽  
Louis J. Everett
Keyword(s):  
Differential Equations ◽  
Configuration Space ◽  
Lagrange Multipliers ◽  
System Modeling ◽  
Constrained Systems ◽  
Minimal Set ◽  
Modeling Methodology ◽  
Hybrid Differential Equations ◽  
Nonlinear Hybrid ◽  
Constrained Devices

Abstract Mechanisms are inherently constrained devices. Combining flexibility with mechanisms usually requires using Lagrange multipliers to handle the constraints. The added algebraic or numerical tedium, associated with the Lagrange multipliers, is well documented. Presented in this paper is a technique for obtaining the minimal set of hybrid parameter differential equations for a constrained device. That is, the set of equations that inherently incorporate the constraints. The technique illustrated in this paper is a recently developed hybrid parameter multiple body (HPMB) system modeling methodology. The variational nature of the methodology allows rigorous equation formulation providing not only the complete nonlinear, hybrid differential equations, but also the boundary conditions. The methodology is formulated in the constraint-free subspace of the system’s configuration space, thus Lagrange multipliers are not needed for constrained systems, regardless of the constraint type (holonomic or nonholonomic). To evince the utility of the method, a flexible four bar mechanism is modeled. Particularly, the inversion of the slider crank found in the quick return mechanism. A comparison of Hamilton’s principle and the described technique, as they are applied to the mechanism, is included. It is shown that the same equations result from either method, but the new technique is much more concise, more efficiently handles the constraints, and requires less algebraic tedium.

Reexamining the tropical Atlantic influence on ENSO using perfect model predictability experiments

2021 ◽  
Author(s):  
Ingo Richter ◽  
Yu Kosaka ◽  
Hiroki Tokinaga ◽  
Shoichiro Kido
Keyword(s):  
Initial Conditions ◽  
Boreal Summer ◽  
Similar Amount ◽  
Tropical Atlantic ◽  
Equatorial Atlantic ◽  
Boreal Spring ◽  
Modes Of Variability ◽  
Control Simulation ◽  
Starting Point ◽  
Perfect Model

<p>The potential influence of the tropical Atlantic on the development of ENSO has received increased attention over recent years. In particular equatorial Atlantic variability (also known as the Atlantic zonal mode or AZM) has been shown to be anticorrelated with ENSO, i.e. cold AZM events in boreal summer (JJA) tend to be followed by El Niño in winter (DJF), and vice versa for warm AZM events. One problem with disentangling the two-way interaction between the equatorial Atlantic and Pacific is that both ENSO and the AZM tend to develop in boreal spring (MAM).</p><p>Here we use a set of GCM sensitivity experiments to quantify the strength of the Atlantic-Pacific link. The starting point is a 1000-year free-running control simulation with the GFDL CM 2.1 model. From this control simulation, we pick years in which a cold AZM event in JJA is followed by an El Niño in DJF. These years serve as initial conditions for “perfect model” prediction experiments with 10 ensemble members each. In the control experiments, the predictions evolve freely for 12 months from January 1 of each selected year. In the second set of predictions, SSTs are gradually relaxed to climatology in the tropical Atlantic, so that the cold AZM event is suppressed. In the third set of predictions, we restore the tropical Pacific SSTs to climatology, so that the El Niño event is suppressed.</p><p>The results suggest that, on average, the tropical Atlantic SST anomalies increase the strength of El Niño in the following winter by about 10-20%. If, on the other hand, El Niño development is suppressed, the amplitude of the cold AZM event also reduces by a similar amount. The results suggest that, in the context of this GCM, the influence of AZM events on ENSO development is relatively weak but not negligible. The fact that ENSO also influences the AZM in boreal spring highlights the complex two-way interaction between these two modes of variability.</p>

scholarly journals Decision making in reverse logistics using system dynamics

2004 ◽  
Vol 14 (2) ◽  
pp. 259-272 ◽  
Author(s):  
P. Georgiadis ◽  
D. Vlachos
Keyword(s):  
Decision Making ◽  
System Dynamics ◽  
Reverse Logistics ◽  
Closed Loop ◽  
System Modeling ◽  
New Approach ◽  
Helpful Tool ◽  
Starting Point ◽  
Decision Making Tool

Reverse logistics is a modern field of consideration, research and study, providing helpful information on the operation of the closed-loop supply chain. Although the starting point of this field is traced back to the early 90?s, no standard method has been suggested, neither prevailed. The purpose of this paper is to introduce a new approach on the study of reverse logistics. It is actually a review on how System Dynamics (SD) can be a helpful tool when it is used in the reverse logistics field. The paper explains the basic theory of the system modeling and next it utilizes the reverse logistics model. Finally, an illustrative example shows how SD modeling can be used to produce a powerful long-term decision-making tool.

scholarly journals Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation.

2006 ◽  
Vol 53 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Ramón Varón ◽  
Matilde E Fuentes ◽  
Manuela García-Moreno ◽  
Francisco Garcìa-Sevilla ◽  
Enrique Arias ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Time Course ◽  
Initial Conditions ◽  
Reaction Scheme ◽  
Complete Analysis ◽  
Zymogen Activation ◽  
Relative Contribution ◽  
Starting Point ◽  
Definition Of

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.

Visualising the invisible: performing chaos theory

Leonardo ◽  
2020 ◽  
pp. 1-8
Author(s):  
Emma Weitkamp
Keyword(s):  
Complex Systems ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Starting Point ◽  
Weather And Climate ◽  
Butterfly Effect ◽  
Long Term Behavior ◽  
The Invisible

Edward Lorenz, the pioneering figure in the field of chaos theory coined the phrase “butterfly effect” and posed the famous question “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?” In posing the question, Lorenz sought to highlight the intrinsic difficulty of predicting the long term behavior of complex systems that are sensitive to initial conditions, like, for example, the weather and climate; these systems are often referred to as chaotic. Taking Lorenz' butterfly as a starting point, Chaos Cabaret sought to explore the nuances of chaos theory through performance and music.

Numerical Computation of Differential-Algebraic Equations for the Approximation of Artificial Satellite Trajectories and Planetary Ephemerides

1999 ◽  
Vol 67 (3) ◽  
pp. 574-580 ◽  
Author(s):  
B. Fox ◽  
L. S. Jennings ◽  
A. Y. Zomaya
Keyword(s):  
Differential Equations ◽  
Virtual Work ◽  
Initial Conditions ◽  
Artificial Satellite ◽  
System Modeling ◽  
Differential Algebraic Equations ◽  
The Body ◽  
Time Interval ◽  
Differential Algebraic Equation ◽  
Generalized Coordinates

The principle of virtual work and Lagrange’s equations of motion are used to construct a system of differential equations for constrained spatial multibody system modeling. The differential equations are augmented with algebraic constraints representing the system being modeled. The resulting system is a high index differential-algebraic equation (DAE) which is cast as an ordinary differential equation (ODE) by differentiating the constraint equations twice. The initial conditions are the heliocentric rectangular equatorial generalized coordinates and their first time derivatives of the planets of the solar system and an artificial satellite. The ODE is computed using the integration subroutine LSODAR to generate the body generalized coordinates and time derivatives and hence produce the planetary ephemerides and satellite trajectories for a time interval. Computer simulation and graphical output indicate the satellite and planetary positions and the latter may be compared with those provided in the Astronomical Almanac. Constraint compliance is investigated to establish the accuracy of the computation. [S0021-8936(00)03403-6]

An Adaptive Vent System for Localized and Customized Thermal Management in Buildings

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Cem Keskin ◽  
M. Pinar Mengüç
Keyword(s):  
Temperature Distribution ◽  
Thermal Management ◽  
System Modeling ◽  
Ventilation System ◽  
Control Unit ◽  
Thermal Conditions ◽  
User Preferences ◽  
User Engagement ◽  
Design Development ◽  
Modeling Methodology

Abstract This paper introduces an innovative ventilation system that is capable of providing localized and customized thermal conditions in buildings. The system has diffusers with individually operable flaps that facilitate asymmetric air inlet to control air flow inside a room in an effective way. Moreover, the system involves distributed temperature sensors, a user interface, and a control unit that allows creation and management of “thermal subzones” within a room in accordance with the different preferences of occupants. As a specific case, the thermal management of a typical office in an academic building is considered. Both experimental and numerical studies were conducted to show that it is possible to achieve several degrees of temperature differences at different room locations in a transient and controllable fashion. The dynamic management of the temperature distribution in a room can prevent the waste of conditioning energy. It is shown that the system provides a practical and impactful solution by adapting to different user preferences (UPs) and by minimizing the resource use. In order to deal with the complexity of design, development, and operation of the system, it is considered as a cyber-physical-social system (CPSS). The core of the CPSS approach used here is an enhanced hybrid system modeling methodology that couples human dimension with formal hybrid dynamical modeling. Based on a coherent conceptual framing, the approach can combine the three core aspects, like cyber infrastructure, physical dynamics, and social/human interactions of modern building energy systems to accommodate the environmental challenges. Besides physics-based achievements (managing temperature distribution inside a room), the new AVS can also leverage user engagement and behavior change for energy efficiency in buildings by facilitating a new practice for occupants' interaction with heating, ventilation, and air conditioning (HVAC) system.

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