Relevant bibliographies by topics / Pendulum – Isochronism – Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Pendulum – Isochronism – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Pendulum – Isochronism – Mathematical models"

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Utomo, Rukmono Budi. "MODEL MATEMATIKA GERAK PENDULUM DENGAN MEMPERTIMBANGKAN GAYA GESEK UDARA." Jurnal Ilmiah Matematika dan Pendidikan Matematika 8, no. 2 (2016): 19. http://dx.doi.org/10.20884/1.jmp.2016.8.2.2884.

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This paper aims to construct a mathematical model of the pendulum motion by considering the frictional force of air. The study was conducted by first making a pendulum motion illustration with a length of rope and pendulum mass vertically that given deviation and speed. Based on that created a mathematical model of motion of the pendulum and its determination to find out the time it takes the pendulum passing through the zero point and the current time there is no change in the speed deviation of the pendulum. In this study will also be given a simulation of mathematical models that have been
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Landa, Polina S. "Universality of oscillation theory laws. types and role of mathematical models." Discrete Dynamics in Nature and Society 1, no. 2 (1997): 99–110. http://dx.doi.org/10.1155/s1026022697000113.

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The universality of oscillation theory laws is discussed. It is suggested that all models of concrete systems be separated into four categories: models – “portraits” of investigated systems, models of the type of “black box”, aggregating models, and models of certain phenomena which can occur in real systems. As an example of the model of the fourth type, the equation of oscillations of a pendulum with a randomly vibrating suspension axis is considered for the purpose of clarifying the mechanism of the transition to turbulence.
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Siradjuddin, Indrazno, Zakiyah Amalia, Erfan Rohadi, et al. "State-feedback control with a full-state estimator for a cart-inverted pendulum system." International Journal of Engineering & Technology 7, no. 4.44 (2018): 203. http://dx.doi.org/10.14419/ijet.v7i4.44.26985.

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A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-
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Jadlovský, Slávka, and Ján Sarnovský. "Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach." Journal of Electrical Engineering 64, no. 1 (2013): 12–19. http://dx.doi.org/10.2478/jee-2013-0002.

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The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for the base and all pendulum links in a generalized (n-link) classical and rotary inverted pendulum system, are implemented in form of symbolic MATLAB functions and a MATLAB GUI application. The validity a
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Monir, Md. "Analyzing and Designing Control System for an Inverted Pendulum on a Cart." European Scientific Journal, ESJ 14, no. 6 (2018): 387. http://dx.doi.org/10.19044/esj.2018.v14n6p387.

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It is a collection of MATLAB functions and scripts, and SIMULINK models, useful for analyzing Inverted Pendulum System and designing Control System for it. Automatic control is a growing field of study in the field of Mechanical Engineering. This covers the proportional, integral and derivative (PID). The principal reason for its popularity is its nonlinear and unstable control. The reports begin with an outline of research into inverted pendulum design system and along with mathematical model formation. This will present introduction and review of the system. Here one dimensional inverted pen
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Yaroslavsky, Danil, Van Vu Nguyen, Marat Sadykov, Mikhail Goryachev, Dmitry Ivanov, and Nikolay Andreev. "Determination the conductor sag according to the period of own harmonic oscillations." E3S Web of Conferences 220 (2020): 01036. http://dx.doi.org/10.1051/e3sconf/202022001036.

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The article substantiates the relevance of the inspection of overhead power lines by determining the mechanical loads of the conductors. The conductor sways under the action of external loads and variable internal mechanical loads. The conductor behaves in span like a pendulum. A model of the harmonic oscillations of the conductor in flight is derived to assess the mechanical loads of the conductor overhead power lines. This mathematical model is based on mathematical models of a flexible thread and a model of a physical pendulum. A conductor is a physical pendulum, where the conductor acts as
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Dominik, Ireneusz. "Fuzzy Logic Control of Rotational Inverted Pendulum." Solid State Phenomena 177 (July 2011): 84–92. http://dx.doi.org/10.4028/www.scientific.net/ssp.177.84.

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The rotational inverted pendulum is a structure that was primarily developed by Katsuhisa Furuta. It is widely used thorough the control laboratories to demonstrate the effectiveness of nonlinear control algorithms. The rotational inverted pendulum is a nonlinear system of fourth order with a single input variable. In this article the full dynamic equations of motion of the rotational inverted pendulum are derived using Lagrangian formulation. Consequently, a comparison of obtained mathematical model with other models described and available in literature is conducted by means of computer simu
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Syuhri, Skriptyan Noor Hidayatullah, and Nasrul Ilminnafik. "Damping Force and Energy Regeneration Characteristics of the Regenerative Pendulum Vibration Absorber." Applied Mechanics and Materials 865 (June 2017): 434–41. http://dx.doi.org/10.4028/www.scientific.net/amm.865.434.

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This paper presents the characteristics of damping force and energy regeneration of a pendulum. The damping force analysis includes force-displacement and force velocity loops when the pendulum, attached in a cart, is subjected with sinusoidal displacement input. The energy regeneration analysis includes the voltage, the current and the power generated by a generator. The main objectives of this paper are to obtain the mathematical models and to characterize both force and energy regeneration based on the inputs. The results show that the amplitudes and the frequencies at low level are most li
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Yuan, Shao Qiang, and Xin Xin Li. "Modeling and Analyses of the N-Link Bent-Arm PenduBot." Advanced Materials Research 171-172 (December 2010): 644–47. http://dx.doi.org/10.4028/www.scientific.net/amr.171-172.644.

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Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.
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Bernhardt, Knut. "Finding Alternatives and Reduced Formulations for Process-Based Models." Evolutionary Computation 16, no. 1 (2008): 63–88. http://dx.doi.org/10.1162/evco.2008.16.1.63.

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This paper addresses the problem of model complexity commonly arising in constructing and using process-based models with intricate interactions. Apart from complex process details the dynamic behavior of such systems is often limited to a discrete number of typical states. Thus, models reproducing the system's processes in all details are often too complex and over-parameterized. In order to reduce simulation times and to get a better impression of the important mechanisms, simplified formulations are desirable. In this work a data adaptive model reduction scheme that automatically builds sim
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Dissertations / Theses on the topic "Pendulum – Isochronism – Mathematical models"

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Eroz, Murat. "Advanced models for sliding seismic isolation and applications for typical multi-span highway bridges." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19709.

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Thesis (Ph.D)--Civil and Environmental Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: DesRoches, Reginald; Committee Member: Goodno, Barry; Committee Member: Jacobs, Laurence; Committee Member: Streator, Jeffrey; Committee Member: White, Donald.
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Sedebo, Getachew Temesgen. "The dynamics of a forced and damped two degrees of freedom spring pendulum." 2013. http://encore.tut.ac.za/iii/cpro/DigitalItemViewPage.external?sp=1001091.

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M. Tech. Mathematical Technology.<br>Discusses the main problems in terms of how to derive mathematical models for a free, a forced and a damped spring pendulum and determining numerical solutions using a computer algebra system (CAS), because exact analytical solutions are not obvious. Hence this mini-dissertation mainly deals with how to derive mathematical models for the spring pendulum using the Euler-Lagrange equations both in the Cartesian and polar coordinate systems and finding solutions numerically. Derivation of the equations of motion are done for the free, forced and damped cases o
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Book chapters on the topic "Pendulum – Isochronism – Mathematical models"

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Náprstek, Jiří, and Cyril Fischer. "A Ball-Type Passive Tuned Mass Vibration Absorber for Response Control of Structures under Harmonic Loading." In Vibration Control of Structures [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.97231.

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Ball-type tuned mass absorbers are growing in popularity. They combine a multi-directional effect with compact dimensions, properties that make them attractive for use at slender structures prone to wind excitation. Their main drawback lies in limited adjustability of damping level to a prescribed value. Insufficient damping makes ball-type absorbers more prone than pendula to objectionable effects stemming from the non-linear character of the system. Thus, the structure and design of the damping device have to be made so that the autoparametric resonance states, occurrence of which depends on system parameters and properties of possible excitation, are avoided for safety reasons. This chapter summarises available 3D mathematical models of a ball-pendulum and introduces the non-linear approach based on the Appell–Gibbs function. Efficiency of the models is then illustrated for the case of kinematic and random excitation. Interaction of the absorber and the harmonically forced simple linear structure is numerically analysed. Finally, the chapter provides examples of typical patterns of the autoparametric response and outlines possibilities of applications in practical engineering.
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Conference papers on the topic "Pendulum – Isochronism – Mathematical models"

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Yesilli, Melih C., and Firas A. Khasawneh. "Data Driven Model Identification for a Chaotic Pendulum With Variable Interaction Potential." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22597.

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Abstract Data driven model identification methods have grown increasingly popular due to enhancements in measuring devices and data mining. They provide a useful approach for comparing the performance of a device to the simplified model that was used in the design phase. One of the modern, popular methods for model identification is Sparse Identification of Nonlinear Dynamics (SINDy). Although this approach has been widely investigated in the literature using mostly numerical models, its applicability and performance with physical systems is still a topic of current research. In this paper we
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Lu, Xiaoxiao, and Justin Seipel. "A Rotary-Leg Robot Model That Predicts Both Leg Revolution and Oscillation Behavior." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65649.

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The Clock-Torqued Spring-Loaded Inverted Pendulum (CT-SLIP) model is extended to predict both leg revolution and oscillation behaviors. With this model we demonstrate that the center-of-mass locomotion dynamics of both leg revolution and oscillation cases have identical local stability with respect to small perturbations, while global stability (with respect to large perturbations) shows differences. This extension of the CT-SLIP model and comparative analysis has potential benefits in robot path planning where there may be a choice between a leg revolution or oscillation. Further, this analys
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Masoud, Ziyad N., Nader A. Nayfeh, and Ali H. Nayfeh. "Sway Reduction on Container Cranes Using Delayed Feedback Controller: Simulations and Experiments." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48571.

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Traditionally, container cranes are modeled as a simple pendulum with a lumped mass at the end of a cable. In the case of large container cranes, the actual configuration of the hoisting mechanism is significantly different; it consists typically of a set of four hoisting cables. These cables are hoisted from four different points on the trolley and are attached on the load side to four points on a spreader bar used to lift containers. The dynamics of the actual hoisting assembly of a container crane is different from that of a simple pendulum. A controller design based on the actual model wil
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Chagdes, James R., Joao P. Freire, and Amit Shukla. "Nonlinear Dynamics of Upright Human Balance While Using a Passive-Cane." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9863.

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Recent mathematical models of human posture have been explored to better understand the space of control parameters that result in stable upright balance. These models have demonstrated that there are two types of instabilities — a leaning instability and an instability leading to excessive oscillation. While these models provide insight into the stability of upright bipedal stance, they are not sufficient for individuals that require the aid of assistive technologies, such as a passive-cane or a walker. Without a valid model one is unable to understand the control parameters required for main
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