The dynamics of bells as impacting system

Author(s):  
T Küpper ◽  
H A Hosham ◽  
K Dudtschenko

The dynamics of impacting systems is the topic of this research study. As a familiar example of a simple impacting device, which can be used to demonstrate well-known features, the motion of a bell is analysed. Based on the abstract modelling as a double pendulum with state-dependent impacts given by the strikes of the clapper onto the bell, various forms are derived. In particular, it is shown that the size of the ‘coupling’ between clapper and bell determines the form of the oscillations showing such phenomena as falling or flying clapper, chatter, and the spectacular case of non-ringing which occurred in the case of the famous emperor's bell in the Cathedral of Cologne. Besides the specific results concerning the motion of the bell, the example can serve as a simple illustration of complicated dynamics in the presence of impacts.

Author(s):  
Hari M Nair ◽  
C Sujatha

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.


2021 ◽  
Vol 2137 (1) ◽  
pp. 012032
Author(s):  
Xisen Wang

Abstract This paper describes the intrinsic qualities of a simple double pendulum (DP), with a visual representation, a rigorous deduction of the Lagrangian equation, and a concrete factor analysis. LSTM model was utilized to simulate the double pendulum’s periodic and chaotic behaviors and evaluates the effectiveness of the model. The auto-correlation coefficients was calculated. Meanwhile, Box-Pierce test and Ljung-Box tests for various state-dependent time series were conducted to give various initial conditions to explore the DP system’s random characteristics. The research results are as follows: 1) Chaos did not lead to direct randomness; 2) seasonality could coexist with chaos; 3) the highly auto-regressive nature of DP’s time series data are found. Therefore, it can be concluded that the chaos in a double pendulum has particular patterns (such as the positive relationship with the likelihood of being a random white noise series) that could be further explored.


2013 ◽  
Vol 53 (6) ◽  
pp. 883-889 ◽  
Author(s):  
Zdenek Neusser ◽  
Michael Valášek

This paper deals with controlling the swing-up motion of the double pendulum on a cart using a novel control. The system control is based on finding a feasible trajectory connecting the equilibrium positions from which the eigenfrequencies of the system are determined. Then the system is controlled during the motion between the equilibrium positions by the special harmonic excitation at the system resonances. Around the two equilibrium positions, the trajectory is stabilized by the nonlinear quadratic regulator NQR (also known as SDRE – the State Dependent Riccati Equation). These together form the control between the equilibrium positions demonstrated on the double pendulum on a cart.


Crisis ◽  
2020 ◽  
Vol 41 (5) ◽  
pp. 367-374
Author(s):  
Sarah P. Carter ◽  
Brooke A. Ammerman ◽  
Heather M. Gebhardt ◽  
Jonathan Buchholz ◽  
Mark A. Reger

Abstract. Background: Concerns exist regarding the perceived risks of conducting suicide-focused research among an acutely distressed population. Aims: The current study assessed changes in participant distress before and after participation in a suicide-focused research study conducted on a psychiatric inpatient unit. Method: Participants included 37 veterans who were receiving treatment on a psychiatric inpatient unit and completed a survey-based research study focused on suicide-related behaviors and experiences. Results: Participants reported no significant changes in self-reported distress. The majority of participants reported unchanged or decreased distress. Reviews of electronic medical records revealed no behavioral dysregulation and minimal use of as-needed medications or changes in mood following participation. Limitations: The study's small sample size and veteran population may limit generalizability. Conclusion: Findings add to research conducted across a variety of settings (i.e., outpatient, online, laboratory), indicating that participating in suicide-focused research is not significantly associated with increased distress or suicide risk.


Author(s):  
Carmen García-Alba

This study is part of a larger research study (doctoral dissertation), in which a comparative study with adolescent samples is done: 50 anorexic restricting patients (ANP), 50 patients diagnosed with depression (DP) and 50 non patients (NP). The proposed objective is two-fold: 1) To try to clarify the existing relationship between Anorexia (AN) and Depression (D), investigated from diverse disciplines but without conclusive results. 2) To detect in the ANP personality different traits from those of other groups, which should, if possible, allow to detect them at an early stage for an adequate prognosis. The current article presents the Rorschach findings in relation to the cognitive functioning of the ANP. In them, the following has been detected: (1) An information processing similar to that of the other groups, even with a more complete (L ≤ .99), more complex (DQ+↑) and better discriminated (Zd↑) grasp of the stimulus; (2) Mediating processes very similar to those of the other groups, sharing with them the perceptive maladjustments (X–%↑) and an excessive individualism (Xu%↑); (3) A clearly differentiating ideation disorder. Definitely, the ANP use predominantly ideation (M↑), but their thought, usually well-adjusted (MQo↑), presents eventual operations of delusional type (MQnone↑). Above that, their thinking is marked by a great passivity (Mp↑), which makes them more vulnerable to accept ideas without criticizing them and it results in a very inefficient thinking, which spins around these concepts without finding solutions, entering into a sort of ruminating which is completely unproductive. The differences toward the obsessive pathology are established. The discriminant analysis conducted with all the Rorschach variables that resulted as significant throughout the research, provides quite a consistent function which discriminates the ANP: MQnone↑, Mp↑, FD↓, Ma↑, MQo↑, AdjD↑, Sum H↑, (H)↑. Based on this we can understand that these adolescents, being in a developmental period of big changes and disorientations in relation with their own image, confronted with life events, and possibly starting off with some biologic vulnerability: (1) Due to the alterations of their ideation, accept without criticism (Mp) irrational ideas dominating in our culture, in which slimness appears as the only model, synthesis of intelligence, beauty and success; remaining captured in this type of mental activity (MQnone), which they cannot escape nor criticize (Mp), despite they reason adequately on other topics (MQo); (2) Their alterations of self-perception [(H)] make them hide themselves in a fantasized image, which is the axis of their interests and the only thing that really matters to them; (3) The resources they have to decide on behaviors and to finish these deliberately (AdjD), and their scarce tendency to the introspection (FD) lead to their decision of not eating, based on distorted and passively accepted thinking, which has great power and thus, so difficult to modify. Finally, based on the Rorschach data obtained, the hypothesis of a personality disorder as underlying pathology is pointed out.


Author(s):  
Andrew Jones ◽  
Samantha Weston ◽  
Alison Moody ◽  
Tim Millar ◽  
Laura Dollin ◽  
...  

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