scholarly journals Mathematical formulation of a dynamical system with dry friction subjected to external forces

2021 ◽  
Vol 421 ◽  
pp. 132859
Author(s):  
A. Bensoussan ◽  
A. Brouste ◽  
F.B. Cartiaux ◽  
C. Mathey ◽  
L. Mertz
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
Mathematical Formulation ◽  
External Forces

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

Study on the Hamilton Dynamical System of Wheel-and-Rail Dynamical Model of High-Speed Train

2015 ◽  
Vol 713-715 ◽  
pp. 99-102
Author(s):  
Hong Yun Shen ◽  
Jian Hua Du ◽  
Yu Lin Wang
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
High Speed ◽  
Dynamical Model ◽  
High Speed Train ◽  
Damping Force ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Practical Engineering

The study on dynamical model of wheel and rail of high-speed train has attracted many researchers nowadays. According to the damping force and the dry friction between wheel and rail, the dynamical model of wheel and rail of high-speed train is constructed and the Hamilton dynamical system of this model is analyzed to discuss its nonlinear dynamical behaviors, which will benefit the practical engineering of high-speed train.

scholarly journals Systems of Oscillators Designed for a Specific Conscious Percept

2020 ◽  
Vol 16 (01) ◽  
pp. 73-88
Author(s):  
Pavel Kraikivski
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Distance Matrix ◽  
Neural Correlates ◽  
Neural Dynamics ◽  
Neural Correlates Of Consciousness ◽  
Oscillatory Processes

As put forward by neuroscientists, the mechanisms of consciousness can be elucidated by revealing correlations between neural dynamics and specific conscious percepts. Recently, I have elaborated on the mathematical formulation for a system of processes that are mutually connected to be isomorphic to a conscious percept of a point in space. Importantly, in such a system, any process can be derived through all other processes that form its complement, or “interpretation.” To generate such a solution, I am proposing a dynamical system of oscillators coupled in a manner to preserve the properties of a percept. Specifically, I crafted a dynamical system that retains the mutual relationships among processes, forming an operational map isomorphic to a distance matrix that mimics a percept of space-like properties. The study and results pave a novel way to analyze the dynamics of neural-like (oscillatory) processes with a purpose of extracting the information relevant to specific conscious percepts, which will facilitate the search for neural correlates of consciousness.

Pullback and Uniform Exponential Attractors for Nonautonomous Boussinesq Lattice System

2015 ◽  
Vol 25 (08) ◽  
pp. 1550100 ◽  
Author(s):  
Min Zhao ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
Boussinesq Equations ◽  
Lattice System ◽  
Time Dependent ◽  
Pullback Attractor ◽  
Exponential Attractor ◽  
Uniform Attractor ◽  
Exponential Attractors ◽  
Lattice Dynamical System ◽  
External Forces

We first prove the existence of a pullback attractor and a pullback exponential attractor for a nonautonomous lattice dynamical system of nonlinear Boussinesq equations affected by time-dependent coupled coefficients and forces. Then, we prove the existence of a uniform attractor and a uniform exponential attractor for the system driven by quasi-periodic external forces.

scholarly journals On the nonsmooth dynamics of towed wheels

Meccanica ◽  
2020 ◽  
Vol 55 (12) ◽  
pp. 2523-2540 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
Three Dimensional ◽  
Nonsmooth Dynamics ◽  
Filippov Systems ◽  
Dimensional Dynamical System ◽  
Creep Models

AbstractIn this paper, a nonsmooth model of towed wheels is analysed; this mechanism can be a part of different kind of vehicles. We focus on the transitions between slipping and rolling in the presence of dry friction. The model leads to a three-dimensional dynamical system with a codimension-2 discontinuity. The systems can be analysed by means of the tools of extended Filippov systems. The essence of the calculation is to find the so-called limit directions, which show the possible directions of slipping-rolling transitions and their properties. By this method, four different scenarios are found. The results are compared to those from the creep models.

The Preliminary Study on Wheel-and-Rail Dynamical Model of High-Speed Train

2014 ◽  
Vol 1082 ◽  
pp. 501-504
Author(s):  
Jian Hua Du ◽  
Hong Yun Shen ◽  
Yu Lin Wang
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
Theoretical Basis ◽  
High Speed ◽  
Dynamical Model ◽  
High Speed Train ◽  
Damping Force ◽  
Preliminary Study

the study on dynamical model of wheel and rail of high-speed train is a focus nowadays. In this paper, the dynamical model of wheel and rail of high-speed train is constructed according to the damping force and the dry friction between wheel and rail. The dynamics of the model was studied and the dynamical system of wheel and rail without collision was analyzed, which povides the theoretical basis for engineering.

On the consistency of a constrained dynamical system with external forces

1982 ◽  
Vol 33 (2) ◽  
pp. 57-61
Author(s):  
A. Z. Capri ◽  
M. Kobayashi
Keyword(s):  
Dynamical System ◽  
External Forces
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