Please use this identifier to cite or link to this item: `http://hdl.handle.net/11455/2754`
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dc.contributor.author黃健楠zh_TW
dc.contributor.authorHuang, Jiann-Nanen_US
dc.date1999zh_TW
dc.date.accessioned2014-06-05T11:43:53Z-
dc.date.available2014-06-05T11:43:53Z-
dc.identifier.urihttp://hdl.handle.net/11455/2754-
dc.description.abstract本文的目的在解決受拘束(constraint)條件下，多體(multibody)機械系統數值積分的穩定性問題。多體系統之運動方程式是一個包含外力、拘束力、加速度的混合微分、代數方程式(mixed differential-algebraic equations，簡稱DAE)，在使用數值積分法解開微分方程式的同時，其位置及速度必須滿足拘束運動方程式及速度運動方程式，也就是說積分的變數是相關的。然而一般的數值積分法並不考慮其中的相關性，直接求解因此造成數值的偏差。 為了解決此問題，Baumgarte嘗試將加速度方程式加入位置項及速度項，當適當的選擇兩項之係數後，數值積分將獲得正確的解，稱為拘束穩定方法(constraint stabilization method)，不過此方法唯一缺點在於係數之選擇，並無規則可循。本文將針對拘束穩定法這部份的研究成果，引入假積分(pseudo-integration)的觀念，並利用數位控制理論中的系統穩定度分析，針對數值積分法中最常用的兩種方法－Predictor-Corrector及Runge-Kutta法，提出一個正確選擇係數的方法。zh_TW
dc.description.abstractThe objective of this project is to resolve the stability problem for the numerical integration of constrained multibody mechanical systems. The dynamic equations of motion of the constrained multibody mechanical system is a mixed differential-algebraic equation(DAE) which contains external forces, constraint reaction forces as well as acceleration of the generalized coordinates of the system. In applying numerical integration methods to solve the mixed differential-algebraic equation, the constraint equation and its first and second derivatives must be satisfied simultaneously. That is, the generalized coordinates are dependent. Direct integration methods do not consider this dependency and constraint violation occurs. To solve this problem, Baumgarte proposed a constraint stabilization method in which a velocity term and a position term were added in the second derivative of the constraint equation. The disadvantage of this method is that there is no known reliable method for selecting the coefficients of the position and velocity term. Improper selection of these coefficients can lead to erroneous results. In this paper, we will use the so-called pseudo-integration equation to analyse the constraint stabilization method for numerical integration. The stability analysis methods in digital control theory will be used to give correct choice of the coefficients for the Adams predictor-corrector and Runge-Kutta method.en_US
dc.description.tableofcontents第一章 緒論1 1.1 前言1 1.2 文獻回顧2 1.3 論文大綱4 第二章 運動方程式與數值積分法5 2.1 動態方程式簡介5 2.2 數值積分法之介紹6 2.2.1 Adams-Bashforth, Adams-Moulton, Predictor-Corrector數值積分法7 2.2.2 Runge-Kutta數值積分法8 2.3 DAE方程式的求解9 2.3.1 直接積分法9 2.3.2 廣義座標分隔法10 2.3.3 拘束穩定法11 2.3.4 混合法12 第三章 數值積分穩定法之理論分析14 3.1 假積分的應用14 3.1.1 Adams-Bashforth積分法15 3.1.2 Adams-Moulton積分法16 3.1.3 Runge-Kutta積分法17 3.2 離散系統之穩定度分析17 3.3 Adams-Bashforth數值積分法19 3.4 Adams Predictor-Corrector數值積分法 －使用拘束穩定法α、β二參數23 3.4.1 一階predictor配合二階corrector23 3.4.2 二階predictor配合三階corrector24 3.4.3 三階predictor配合四階corrector26 3.5 Adams Predictor-Corrector數值積分法 －使用拘束穩定法α、β、ζ、η四參數31 3.5.1 一階predictor配合二階corrector34 3.5.2 二階predictor配合三階corrector35 3.5.3 三階predictor配合四階corrector37 3.6 Runge-Kutta數值積分法 －使用拘束穩定法42 第四章 實例模擬與驗證45 4.1 曲柄滑塊之實例45 4.2 Predictor-Corrector－使用拘束穩定法α、β二參數47 4.3 Predictor-Corrector－使用拘束穩定法α、β、ζ、η四參數51 4.4 Predictor-Corrector－使用拘束穩定法並配合牛頓法53 4.5 Runge-Kutta－使用拘束穩定法54 第五章 結論與未來展望85 參考文獻86zh_TW
dc.language.isoen_USzh_TW
dc.publisher機械工程學系zh_TW
dc.subject多體機械系統zh_TW
dc.subjectmultibody mechanical systemsen_US
dc.subject數值積分zh_TW
dc.subject混合微分zh_TW
dc.subject代數方程式zh_TW
dc.subject拘束穩定法zh_TW
dc.subject假積分zh_TW
dc.subjectnumerical integrationen_US
dc.subjectdifferential-algebraic equationen_US
dc.subjectconstraint stabilization methoden_US
dc.subjectpseudo-integrationen_US
dc.title多體機械系統使用拘束穩定數值積分法時參數選擇之研究zh_TW
dc.titleParameters Selection of the Constraint Stabilization Method for Numerical Integration of Multibody Mechanical Systemsen_US
dc.typeThesis and Dissertationzh_TW
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item.fulltextno fulltext-
item.cerifentitytypePublications-
item.languageiso639-1en_US-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeThesis and Dissertation-
Appears in Collections:機械工程學系所