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Symplectic Integration of Bar Linkage Motion Equations
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 조맹효 | - |
dc.contributor.author | David Van Isacker | - |
dc.date.accessioned | 2017-07-14T03:41:32Z | - |
dc.date.available | 2017-07-14T03:41:32Z | - |
dc.date.issued | 2016-02 | - |
dc.identifier.other | 000000133727 | - |
dc.identifier.uri | https://hdl.handle.net/10371/123894 | - |
dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 기계항공공학부, 2016. 2. 조맹효. | - |
dc.description.abstract | In this study, the motion and the qualitative behaviour of an unconstrained simple bar-linkage which is under the influence of different types of forces is studied. Standard non-symplectic integration methods are not suited for integrating systems of differential equations over long periods of time. Therefore, symplectic integration algorithms based on the discretization of the Hamilton variational principle are used. Unconstrained multi-body linkages obey to complex motion equations that require adequate numerical integrations. One non-symplectic integration method – the forward Euler method- as well as three different symplectic methods –the discrete midpoint Lagrangian method, the discrete trapezoidal Lagrangian method and the Newmark-β method have been implemented. The advantages of symplectic integrators over non-symplectic integrators for this class of systems including stability, proper qualitative behaviour and energy conservation. The results and the performances of both symplectic and non-symplectic integration methods are analysed and compared, in terms of energy, movement and computational costs. These numerical experiments suggest the use of symplectic methods for conservative and near-conservative multi-body mechanical systems, whereas dissipative systems in general do not require the use of symplectic methods to provide accurate computations. | - |
dc.description.tableofcontents | Chapter 1. Introduction 1
1.1. Symplectic Integration of Differential Equations 1 1.2. Symplectic Resolution of Motion Equation for Bar-Linkage Systems 2 1.3. Variational Integrators 3 Chapter 2. Lagrangian Dynamics 4 2.1. Continuous Lagrangian Dynamics 4 2.2. Discrete Time Lagrangian Dynamics 5 Chapter 3. Symplectic Integration of Differential Equations 8 3.1. Symplectic and Variational integrators 8 3.2. Energy Preservation 10 3.3. Qualitative Physical Behaviour 11 3.4. Accuracy 12 3.5. Formulation of the Variational Algorithm 13 Chapter 4. Application to Multi-body Bar Linkage Systems 16 4.1. Bar-linkage System 16 4.2. Methodology for Symplectic and Non-symplectic Resolution 17 4.3. Free Fall of a 2-Bar Linkage System 18 4.4. Bar Linkage Subjected to a Central Force Potential 22 4.5. Central Force and Dissipative Potential 31 4.6. Computation Time: 35 Chapter 5. Conclusion 37 Bibliography 39 Abstract (Korean) 41 | - |
dc.format | application/pdf | - |
dc.format.extent | 1609409 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Bar Linkages | - |
dc.subject | Discrete Mechanics | - |
dc.subject | Geometric Integration | - |
dc.subject | Multibody Systems | - |
dc.subject | Symplectic Integration | - |
dc.subject | Variational Integrators | - |
dc.subject.ddc | 621 | - |
dc.title | Symplectic Integration of Bar Linkage Motion Equations | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | 데이비드 | - |
dc.description.degree | Master | - |
dc.citation.pages | 42 | - |
dc.contributor.affiliation | 공과대학 기계항공공학부 | - |
dc.date.awarded | 2016-02 | - |
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