2005-08-012024-05-15https://scholars.lib.ntu.edu.tw/handle/123456789/663107摘要：本計畫旨在以理論與實驗之方式研究運動律與組成律的正則架構,包括單一質點與多質點系統的摩擦運動,以及其場論化(連續化、反離散化),即連體的耗散變形與運動。本計畫的重心在於(牛頓與愛因斯坦)運動律的哈氏量(Hamiltonian) 推廣為含(牛頓與愛因斯坦)運動律與(保守與耗散)組成律的哈氏量。冀望由於正則架構之掌握,可以利用正則變換,建構解析正解與高精度保群算法。由於組成律的變率效應與運動律的慣性效應同時出現,因此在實驗時,對於實驗方法與實驗分析(數據處理、模式識別、參數估測)影響很大,本計畫擬研究其理論關係,並據以改進實驗方法與實驗分析方法。<br> Abstract: The project is proposed to study theoretically and experimentally the canonical framework of the laws of motion and constitution for a particle moving or trapped in a frictional environment, and its finitely many degree-of-freedom and continuum versions. The main focus is on the challenging extension of the Hamiltonians of the motion laws of Newton and Eienstein to Hamiltonians which account for both (conservative and dissipative) constitutive laws and (Newtonian and Eienstein) motion laws. Once the canonical framework is at our disposal, we can take advantage of canonical transformations to find exact and analytical solutions and to devise highly accurate group-preserving algorithms. The rate effect of constitutive laws and the inertia effect of the motion laws manifest themselves simultaneously rather than separately; this fact thus has a great influence on the methods of experimentation and experimental analyses --- data processing, model identification, and parameter estimation. Guided by the framework we will study their theoretical relationship, and thereby improve the methods of experimentation and experimental analyses.運動律組成律哈氏量正則變換保群算法場論實驗方法實驗分析變率效應慣性效應塑性摩擦耗散。motion lawconstitutive lawHamiltoniancanonical frameworkgroup-preserving algorithm,