Log in

Relevant bibliographies by topics / Pantograph equation

Contents

Journal articles
Dissertations / Theses
Book chapters
Conference papers

Academic literature on the topic 'Pantograph equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Pantograph equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Pantograph equation"

1

van Brunt, B., A. A. Zaidi, and T. Lynch. "Cell Division And The Pantograph Equation." ESAIM: Proceedings and Surveys 62 (2018): 158–67. http://dx.doi.org/10.1051/proc/201862158.

Full text

Abstract:

Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density. Pantograph equations arise in a number of applications outside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the rôle of the pantograph equation in the context of cell division. In addition, for a simple case we present a method of solution based on the Mellin transform and establish u

APA, Harvard, Vancouver, ISO, and other styles

2

Bryja, Danuta, and Dawid Prokopowicz. "Discrete-continuous computational model of the coupled dynamic system: pantograph – overhead contact line." Transportation Overview - Przeglad Komunikacyjny 2016, no. 5 (2016): 71–83. http://dx.doi.org/10.35117/a_eng_16_05_08.

Full text

Abstract:

The paper presents the computational model of the pantograph – overhead contact line (OCL), which uses the theory of cable vibrations and Lagrange – Ritz approximation method to derive equations of motion of the overhead contact line subjected to moving pantographs. The pantograph is modelled as a dynamic system of two degrees of freedom describing the motion of two masses replacing a collector head and an articulating frame. The overhead contact line is defined as a catenary system with continuously distributed mass. It consists of a multi-span cable characterized by a curvilinear route (cate

APA, Harvard, Vancouver, ISO, and other styles

3

Wilk, Andrzej. "Novel analysis methods of dynamic properties for vehicle pantographs." MATEC Web of Conferences 180 (2018): 01005. http://dx.doi.org/10.1051/matecconf/201818001005.

Full text

Abstract:

Transmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should take into account: mass distribution of particular parts, physical properties of used materials, kinematic joints character at mechanical nodes, nonlinear parameters o

APA, Harvard, Vancouver, ISO, and other styles

4

Jia, Zhifu, Xinsheng Liu, and Yu Zhang. "New stability theorem for uncertain pantograph differential equations." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 9403–11. http://dx.doi.org/10.3233/jifs-201864.

Full text

Abstract:

Uncertain pantograph differential equation (UPDE for short) is a special unbounded uncertain delay differential equation. Stability in measure, stability almost surely and stability in p-th moment for uncertain pantograph differential equation have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concept of stability in distribution, and proves the sufficient condition for uncertain pantograph differential equation being stable in distribution. In addition, the relationships among stability almost surely, stability in mea

APA, Harvard, Vancouver, ISO, and other styles

5

Benet, Jesús, Fernando Cuartero, Tomás Rojo, Pedro Tendero, and Enrique Arias. "A Dynamic Model for the Study and Simulation of the Pantograph–Rigid Catenary Interaction with an Overlapping Span." Applied Sciences 11, no. 16 (2021): 7445. http://dx.doi.org/10.3390/app11167445.

Full text

Abstract:

In this paper, the authors present a mathematical and engineering model to optimally calculate the dynamic equation on the pantograph–catenary interaction when considering a rigid catenary with an overlapping span. The model starts from well-known methods adapted to the special features of rigid catenary. As a result, an algorithm for the integration of a dynamic equation based on explicit methods is provided. Moreover, from this algorithm, a reliable, efficient, and user-friendly software tool called RICATI is developed in order to approach the model to railway-based companies. The results sh

APA, Harvard, Vancouver, ISO, and other styles

6

Jánský, Jiří, and Petr Kundrát. "The stability analysis of a discretized pantograph equation." Mathematica Bohemica 136, no. 4 (2011): 385–94. http://dx.doi.org/10.21136/mb.2011.141698.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Iserles, A. "On the generalized pantograph functional-differential equation." European Journal of Applied Mathematics 4, no. 1 (1993): 1–38. http://dx.doi.org/10.1017/s0956792500000966.

Full text

Abstract:

The generalized pantograph equation y′(t) = Ay(t) + By(qt) + Cy′(qt), y(0) = y0, where q ∈ (0, 1), has numerous applications, as well as being a useful paradigm for more general functional-differential equations with monotone delay. Although many special cases have been already investigated extensively, a general theory for this equation is lacking–its development and exposition is the purpose of the present paper. After deducing conditions on A, B, C ∈ ℂd×d that are equivalent to well-posedness, we investigate the expansion of y in Dirichlet series. This provides a very fruitful form for the

APA, Harvard, Vancouver, ISO, and other styles

8

Liu, Yunkang. "Numerical investigation of the pantograph equation." Applied Numerical Mathematics 24, no. 2-3 (1997): 309–17. http://dx.doi.org/10.1016/s0168-9274(97)00028-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Shapira, Asaf, and Mykhaylo Tyomkyn. "Quasirandom Graphs and the Pantograph Equation." American Mathematical Monthly 128, no. 7 (2021): 630–39. http://dx.doi.org/10.1080/00029890.2021.1926187.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Li, Hua, and Shu Qian Cao. "The Double Pendulum Model and Nonlinear Dynamic Characteristics of the Pantograph of High-Speed Train." Applied Mechanics and Materials 275-277 (January 2013): 767–70. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.767.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic "Pantograph equation"

1

Obrátil, Štěpán. "Vyšetřování stability numerických metod pro diferenciální rovnice se zpožděným argumentem." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-400513.

Full text

Abstract:

The thesis deals with numerical analysis of delay differential equations. Particularly, the -method is applied to the pantograph equation considering equidistant and quasi-geometric mesh. Qualitative properties of the numerical methods are demonstrated on several special cases of the pantograph equation.

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Pantograph equation"

1

Bogachev, Leonid, Gregory Derfel, Stanislav Molchanov, and John Ochendon. "On Bounded Solutions of the Balanced Generalized Pantograph Equation." In Topics in Stochastic Analysis and Nonparametric Estimation. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75111-5_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Bica, Alexandru Mihai, Mircea Curila, and Sorin Curila. "Spline Iterative Method for Pantograph Type Functional Differential Equations." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_16.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Gürbüz, Burcu, and Mehmet Sezer. "Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations." In 4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019). Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39112-6_8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

"4. Analytical Solution of Pantograph Equation with Incommensurate Delay." In Computational Sciences. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110467215-004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Baccari, Silvio, Giulio Cammeo, Christian Dufour, et al. "Real-Time Hardware-in-the-Loop in Railway." In Railway Safety, Reliability, and Security. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-1643-1.ch010.

Full text

Abstract:

The increasing complexity of modern ground vehicles is making crucial the role of control for improving energetic efficiency, comfort and performance. At the same time, the control software must be frequently updated in order to let the vehicle respond safely and efficiently within more sophisticated environments and to optimize the operations when new vehicle components are integrated. In this framework real-time hardware-in-the-loop simulations represent a fundamental tool for supporting the verification and validation processes of the control software and hardware. In this chapter a railway case study will be presented. The mathematical models of the most relevant electromechanical components of the vehicle powertrain are presented: the pantograph connected to an ideal overhead line with continuous voltage; the electrical components of a pre-charge circuit, the line filter and the braking chopper; the three-phase voltage source inverter and the induction motor; and, finally, the mechanical transmission system, including its interactions with the rail. Then the issues related to the real-time simulation of the locomotive components models are discussed, concentrating on challenges related to the stiff nature of the dynamic equations and on their numerical integration by combining field programmable gate array (FPGA) and central processing unit (CPU) boards. The usefulness of the real-time hardware-in-the-loop simulations for the analysis of railway control software will be demonstrated by considering the powertrains of two real metropolitan trains under complex scenarios, i.e., stator winding disconnection of the induction motor, pantograph missing contact, wheel-rail slipping phenomenon.

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Pantograph equation"

1

Appleby, John, and Evelyn Buckwar. "Sufficient conditions for polynomial asymptotic behaviour of the stochastic pantograph equation." In The 10'th Colloquium on the Qualitative Theory of Differential Equations. Bolyai Institute, SZTE, 2016. http://dx.doi.org/10.14232/ejqtde.2016.8.2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Kundrát, Petr. "Discretized Pantograph Equation with a Forcing Term: Note on Asymptotic Estimate." In Proceedings of the Twelfth International Conference on Difference Equations and Applications. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814287654_0024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Hua Yang, Feng Jiang, and Yonghong Jiang. "Robust stability of stochastic pantograph differential equations Markovian switching." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5620312.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Seong, Hoo Yann, and Zanariah Abdul Majid. "Solving delay differential equations of pantograph type using predictor-corrector method." In INTERNATIONAL CONFERENCE ON MATHEMATICS, ENGINEERING AND INDUSTRIAL APPLICATIONS 2014 (ICoMEIA 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4915692.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Hoo Yann Seong and Zanariah Abdul Majid. "Solving neutral delay differential equations of pantograph type by using multistep block method." In 2015 International Conference on Research and Education in Mathematics (ICREM7). IEEE, 2015. http://dx.doi.org/10.1109/icrem.2015.7357026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Seo, Jong-Hwi, Hiroyuki Sugiyama, and Ahmed A. Shabana. "Spatial Finite Element Formulation for the Pantograph/Catenary Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84060.

Full text

Abstract:

This paper describes a three-dimensional large deformation finite element formulation for the analysis of the multibody pantograph/catenary systems. The large deformation of the catenary is modeled using the three-dimensional finite element absolute nodal coordinate formulation. A non-generalized arc-length parameter is introduced in order to be able to formulate the joint between the catenary and pan-head and to accurately predict the location of the contact point. The resulting system of differential and algebraic equations formulated in terms of reference coordinates, finite element absolut

APA, Harvard, Vancouver, ISO, and other styles

7

Yamashita, Kiyotaka, Tomoaki Nakayama, Toshihiko Sugiura, and Hiroshi Yabuno. "Numerical Bifurcation Analysis of Multimode Impact Oscillations Between a Pantograph and a Rigid Conductor Line." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70360.

Full text

Abstract:

This paper deals with the numerical bifurcation analysis of the contact loss between a pantograph and an overhead rigid conductor line in a railway current collection system. In the previous study, we modeled this problem as impact oscillations of an intermediate spring-supported beam excited by an oscillating plate. We have already derived the modal interaction relationship equations that describe the velocities immediately after an impact as functions of the velocities before impact for each vibration mode. A numerical calculation using these relationship equations was performed to clarify t

APA, Harvard, Vancouver, ISO, and other styles

8

Fedorov, Dmitri, and Lionel Birglen. "Analysis and Design of a Two Degree of Freedom Hoeckens-Pantograph Leg Mechanism." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47330.

Full text

Abstract:

Hoeckens and Chebychev linkages have been widely discussed in the literature as design solutions to build single degree of freedom (DOF) leg mechanisms. Compared to fully actuated legs, often bio-inspired, they offer an unmatched simplicity. However, due to their limited motion capability, they can only be used when the traversed terrain is of limited difficulty. In order to alleviate this drawback, a novel design with a second DOF is proposed in this paper. The introduced mechanism is composed of a Hoeckens linkage augmented by a Pantograph for which the position of the pivot can be changed t

APA, Harvard, Vancouver, ISO, and other styles

9

Font-Llagunes, Josep M., and Jo´zsef Ko¨vecses. "Dynamics of Non-Ideal Topology Transitions in Multibody Mechanical Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86883.

Full text

Abstract:

Mechanical systems with time-varying topology appear frequently in various applications. In this paper, topology changes that can be modeled by means of bilateral impulsive constraints are analyzed. We present a concept to project kinematic and kinetic quantities to two mutually orthogonal subspaces of the tangent space of the mechanical system. This can be used to obtain decoupled formulations of the kinetic energy and the dynamic equations at topology transition. It will be shown that the configuration of the multibody system at topology change significantly influences the projection of non-

APA, Harvard, Vancouver, ISO, and other styles

10

Shayan Amin, Sara, and Jo´zsef Ko¨vecses. "Dynamics of Multibody Haptic Systems." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48551.

Full text

Abstract:

An essential requirement in haptics is accuracy and transparency of the haptic interface. Haptic devices are usually lightweight robotic systems with which a human operator interacts. In the current literature, dynamic analyses of haptic devices are limited to single degree-of-freedom (DoF) point mass models. In this paper, experimental and simulation studies are conducted to investigate the effects of mechanical design parameters on the performance of such devices. For this purpose two commonly used haptic devices were considered: a two-DoF PANTOGRAPH and a three-DoF PHANToM. The results show

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!