Numerical Location of Painlevé Paradox-Associated Jam and Lift-Off in a Double-Pendulum Mechanism

2017 ◽  
Vol 12 (6) ◽  
Author(s):  
Shane J. Burns ◽  
Petri T. Piiroinen
Keyword(s):  
Numerical Simulation ◽  
Mechanical System ◽  
Coefficient Of Friction ◽  
Double Pendulum ◽  
Painlevé Paradox ◽  
Forward Solution ◽  
Pendulum System ◽  
Graphical Technique ◽  
Lift Off

In this article, we will introduce the phenomenon known as the Painlevé paradox and further discuss the associated coupled phenomena, jam and lift-off. We analyze under what conditions the Painlevé paradox can occur for a general two-body collision using a framework that can be easily used with a variety of impact laws, however, in order to visualize jam and lift-off in a numerical simulation, we choose to use a recently developed energetic impact law as it is capable of achieving a unique forward solution in time. Further, we will use this framework to derive the criteria under which the Painlevé paradox can occur in a forced double-pendulum mechanical system. First, using a graphical technique, we will show that it is possible to achieve the Painlevé paradox for relatively low coefficient of friction values, and second we will use the energetic impact law to numerically show the occurrence of the Painlevé paradox in the double-pendulum system.

Independent Asymmetric Period-3 Motions in a Periodically Forced Double-Pendulum

2019 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chuan Guo
Keyword(s):  
Numerical Simulation ◽  
Vibration Reduction ◽  
Mapping Method ◽  
Eigenvalue Analysis ◽  
Double Pendulum ◽  
Pendulum System ◽  
Implicit Mapping ◽  
Stability And Bifurcation

Abstract In this paper, the independent asymmetric period-3 motions of a periodically forced, damped, double-pendulum are predicted through a discrete implicit mapping method. The corresponding stability and bifurcation conditions of the paired asymmetric period-3 motions are determined through eigenvalue analysis. Numerical simulation of the two asymmetric period-3 motions in the double-pendulum system is completed from analytical predictions. The example presented herein can be used for the vibration reduction of the first pendulum through the motions of the second pendulum.

Advanced modeling and optimal control of a cart-double pendulum system

2019 ◽  
Author(s):  
◽  
Cecil Jr. Shy
Keyword(s):  
Optimal Control ◽  
Lagrange Equation ◽  
Control Technique ◽  
Tuning Parameter ◽  
Microgravity Environment ◽  
Double Pendulum ◽  
Overhead Crane ◽  
Material Transport ◽  
Pendulum System ◽  
Industry Standards

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The Overhead Crane has evolved in scope since its inception in the late 1800's. Its early use as a hoist for material transport is now proceeded by new found applications, such as in the Active Response Gravity Offload System (ARGOS) at the NASA Johnson Space Center. ARGOS is an astronaut training facility designed to simulate reduced gravity environments such as Lunar, Martian, or microgravity. By industry standards, it is essentially a repurposed Overhead Crane; in academia it can be conceptualized as a cart-double pendulum system. Anti-sway control of cart-pendulum systems has been heavily researched; however, these methods are not typically designed for space simulation. The goal of this research is to design a controller that provides both energy and error minimization for the cart-pendulum, so that its payload moves as if it were floating freely in a microgravity environment (according to Newton's 1st law). The Euler-Lagrange equation is used to model the system and an optimal control technique called the [alpha]-shift is used to control the system. Most treatments on optimal linear control do not include the [alpha]-shift, but its addition allows one to stabilize the system faster and provides an extra tuning parameter while maintaining the simplicity of the solution. Numerical experiments show that the [alpha]-shift method significantly improves the cart-pendulum's ability to control its payload; especially for payloads in the cart-double-pendulum case.

Study on Microscopic Mechanism for Sand Particles Lift-Off

2011 ◽  
Vol 211-212 ◽  
pp. 1147-1151
Author(s):  
A Fang Jin ◽  
Zhi Chun Yang ◽  
Mamtimin Gheni
Keyword(s):  
Numerical Simulation ◽  
Air Flow ◽  
Particle Dispersion ◽  
Sph Method ◽  
Two Phase ◽  
Microscopic Mechanism ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Sand Particles ◽  
Lift Off

Smoothed particle hydrodynamics (SPH) method is used to simulate the lift-off phenomenon of sand particles in the air flow. Whether the sand particles make any form of movement in the air flow, firstly, they always jump into the air from a standstill condition, so it is helpfull to understand the saltation mechanism of sand particles. Because the computitional region is discreted into particles in the SPH method, the movement of each particle can represent the machnical behavior of sand particles if the particle dispersion has the same characteristic with the sand particles. The foundmental theory of SPH method and its key elements are reviewed in detail, such as the kernel function, the choice of smoothing length and their influence on the numerical simulation results.In this study a numerical simulation model of wind-blown sand two-phase flow using SPH model is proposed and then the model is discreted to simulate the take-off process of sand particles with adquate boundary conditions. Simulation results show that the proposed model can be used to simulate the dynamic characteristics of sand particles in lift-off.

Period Motions in a Periodically Forced, Damped Double Pendulum

2018 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chuan Guo
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Mapping Method ◽  
Eigenvalue Analysis ◽  
Double Pendulum ◽  
Implicit Mapping ◽  
Stability And Bifurcation

In this paper, period motions in a periodically forced, damped, double pendulum are analytically predicted through a discrete implicit mapping method. The implicit mapping is established via the discretized differential equation. The corresponding stability and bifurcation conditions of the period motions are predicted through eigenvalue analysis. Numerical simulation of the period motions in the double pendulum is completed from analytical predictions.

Vehicle tip-over prevention using gain-scheduled State-dependent Riccati Equation–based anti-rollover controller

2020 ◽  
pp. 095440702094831
Author(s):  
Hari M Nair ◽  
C Sujatha
Keyword(s):  
Riccati Equation ◽  
Initial Conditions ◽  
Real Life ◽  
Lookup Table ◽  
Computational Time ◽  
Double Pendulum ◽  
Vehicle Model ◽  
State Dependent ◽  
Lift Off ◽  
Gain Scheduled

The most hazardous kind of vehicle crash among all road accidents is vehicle rollover. Present-day rollover prevention systems in commercial vehicles mitigate rollover by preventing any wheel lift-off from the ground. These systems make use of actuators such as differential brakes and demand all the wheels on the ground for satisfactory operation. Such systems are not effective in recovering a vehicle from intense rollover scenarios where the wheels on one side are lifted off the ground, and the vehicle is about to rollover to the other side after reaching the tip-over point. A few studies have investigated the possibility of reinstating a vehicle at the tip-over point with the wheels on a side lifted off. The high complexity and computation time of the optimal control strategies such as nonlinear model predictive controller make it unsuitable for real-time implementations. This study proposes a novel gain-scheduled State-dependent Riccati Equation–based optimal anti-rollover controller for reinstating a vehicle from the tip-over point. An inverted double pendulum on a cart vehicle model is used as the plant model. The anti-rollover controller is found to be presentable as a two-dimensional gain-scheduled lookup table with specific state dependencies in existence. It eliminates the necessity of solving the nonlinear performance index minimization problem online. State-dependent Riccati Equation method adequately accounts for the nonlinearities involved, yet possesses a small computational time per sample. The anti-rollover controller is evaluated with a 10 degrees of freedom full vehicle model with a nonlinear pure slip tyre model that incorporates the dynamical effects neglected in the controller formulation. Finally, the anti-rollover controller is evaluated in real-life initial conditions using a sophisticated pick-up truck model obtained from TruckSim® software through a co-simulation with the anti-rollover controller setup in MATLAB®/Simulink® environment. The State-dependent Riccati Equation controller was found to be effective in reinstating the higher-order models from the tip-over point in all the case studies conducted.

The Double Pendulum Model and Nonlinear Dynamic Characteristics of the Pantograph of High-Speed Train

2013 ◽  
Vol 275-277 ◽  
pp. 767-770
Author(s):  
Hua Li ◽  
Shu Qian Cao
Keyword(s):  
Numerical Simulation ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Lagrange Equation ◽  
Variable Stiffness ◽  
Nonlinear Damping ◽  
Double Pendulum ◽  
High Speed Train ◽  
Pendulum Model ◽  
Damping Torque

In this paper, the double pendulum model of the pantograph was developed, in which a square angular velocity damping torque was used to describe the nonlinear damping torque of the hydraulic vibration damper, and the catenary was described as a variable stiffness spring. Considering the nonlinear factors caused by hydraulic damping and the interaction between the catenary and the pantograph, the motion differential equations based on the double pendulum model were established in Lagrange equation, and then were simplified. The dynamic characteristics were analyzed through numerical simulation. The result of numerical simulation shows that there are quasi-periodic motion and chaos in the system, which are both affected by the pendulum length ratio. The results are helpful to research the dynamic characteristics of the pantograph of high-speed train.

Physics of Flexible Magnetic Filaments

2011 ◽  
Vol 222 ◽  
pp. 221-224 ◽  
Author(s):  
Ivars Javaitis ◽  
Vineta Zilgalve
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Coefficient Of Friction ◽  
Low Frequency ◽  
Rotating Magnetic Field ◽  
Physical Parameters ◽  
Filament Dynamics ◽  
Field Coefficient ◽  
Stable Shape

A model of elastic magnetic filaments is developed, which allows investigating the dependence of filament dynamics on such physical parameters as magnetoelastic number (Cm), frequency of magnetic field, coefficient of friction, etc. By numerical simulation of the dynamics of filament shaping under the action of magnetic field it is shown that a characteristic U-like stable shape (hairpins) can form. Such a shape of filament can exist in the case of low-frequency rotating magnetic field. At the frequency increasing the U-like shape transforms to the S-like one. In the present work it is shown that in unsteady magnetic field a flexible magnetic filament “swims” in the direction of magnetic field.

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