关于力系简化中主矢是不是力的讨论

在国内多数理论力学教材与相关教材里,对任意力系的简化中,均认为主矢不是力,其只是各力的矢量和. 笔者认为这样定义在理论上与实际上无多大意义; 这样定义有前后矛盾、不统一之处; 易使学生在理解上产生疑问与困惑; 易使学生在计算力系简化时产生错误的结果. 因此,笔者认为应明确定义力系简化中的主矢(假如仍用此名称)是力,不用只抽象定义其是各力的矢量和.     

我怎样讲力系等效、简化和平衡——————理论力学教学札记之二

 力系等效简化是理论力学的重要内容, 传统的教学 方法需要较多学时, 对多种情况分类给出很多规则和结论, 针对此问题探讨 改进讲授思路.     

<理论力学>课程体系与教学内容改革的研究与实践--介绍新编教材<静力学与动力学>

介绍了理论力学课程新编教材<静力学与动力学>的特点, 模块式设课和调整内容重点等, 并介绍了结合使用新教材进行教学改革的情况.     

含铝炸药能量释放的简化模型

为了在水下爆炸效应中反映出非理想爆轰特性的影响,建立了含铝炸药非理想爆轰能量释放的简化模型。该模型以CJ爆轰理论和二次反应理论为基础,把含铝炸药化学反应划分为快速反应和慢速反应,以释放的化学能和慢反应速率常数作为非理想特征参数,并应用于一维数值模拟。计算结果与基本实验结果一致,冲击波峰值的计算误差不大于10％,衰减时间常数的误差小于5％,冲击波能与实验值也具有良好的一致性。简化模型合理地描述了含铝炸药非理想爆轰的主要过程及非理想特性,可应用于含铝炸药的设计和爆炸效应的分析。     

谈谈弹塑性力学中的简化问题

讨论了弹塑性力学中的基本假设、本构模型和简化分析方法. 指出在这一领域中, 简化是非常重要的和必需的.     

理论力学课程研究型教学模式的探索与实践

理论力学课程的研究型教学弥补了基础教学课堂在内容方面的缺憾, 在培养大学生的创新精神和工程实践能力方面起到了重要作用. 本文给出了理论力学课程在进行研究型模式探索中的教学设计思路和一些教学实践, 改革了课堂教学, 在提高学生的主动学习意识和积极思维能力方面, 收到了良好的教学效果.     

动量守恒札记

通过对理论力学教材中某一常见习题的分析,阐明判断系统是否存在动量守恒,不仅要看表面现象,更要注意隐藏的动量守恒关系.     

理论力学与计算机计算教学深度改革的实施经验和体会

本文依照四川大学某理论力学教学班实际教学改革的经验,通过具体举例说明计算机技术在理论力学教学中尚未开发的巨大潜力,减小数学运算使学生重点关注理论力学基本原理,批量求解使学生提前接触实际应用案例,普适性求解使学生深化对处理多变量问题的认识。同时本文还探讨了理论力学教学改革的方向和目的,即把教学重点放在普适的教学方法上,借助计算机求解多刚体、多变量问题,以期有助于理论力学教材更好地适应时代发展。     

理论力学课程英译名称引发的思考

现有理论力学课程英文名称普遍译成"TheoreticalMechanics".作者从课程发展的历史主线以及欧美惯用表述出发,提出对此译文的质疑,并进一步探讨分析力学在整个经典力学体系中的地位.针对我国现有理论力学教学现状,比较中美高校理论力学教学内容上的差异,呼吁在高校理论力学教学内容中增加分析力学的比重.在课程教学中,注重力学发展史主线的描绘,帮助学生树立力学学科的历史发展观,以进一步适应人才培养与时代发展需求.     

《漫话动力学》

<正>《漫话动力学》,贾书惠著,高等教育出版社出版,2010年1月第1版,定价19.20元.内容简介:动力学是研究物体机械运动规律的科学,与日常生活、自然现象及工程实践有着广泛的联系.本书从常见的日常现象出     

Global view of microstructural evolution: Energetics,kinetics and dynamical systems

An evolving material structure is in a non-equilibrium state, with free energy expressed by the generalized coordinates. A global approach leads to robust computations for the generalized thermodynamic forces. Those forces drive various kinetic processes, causing dissipation at spots, along curves, surfaces and interfaces, and within volumetric regions. The actual evolution path, and therefore the final equilibrium state, is determined by the energetics and kinetics. A virtual work principle links the free energy landscape and the kinetic processes, and assigns a viscous environment to every point on the landscape. The approach leads to a dynamical system that governs the evolution of generalized coordinates. The microstructural evolution is globally characterized by a basin map in the coordinate space; and by a diversity map and a variety map in the parameter space. The control of basin boundaries raises the issue of energetic and kinetic bifurcations. The variation of basin boundaries under different sets of controlling parameters provides an analytical way to plot the diversity maps of structural evolution. The project supported by the National Science Foundation (USA) through grant MSS-9258115, and by the National Natural Science Foundation of China     

Model order reduction for dynamical systems: A geometric approach

The aim of this paper is to ask the question as whether it is possible, for a given dynamical system defined by a vector field over a finite dimensional inner product space, to construct a reduced-order model over a finite dimensional manifold. In order to give a positive answer to this question, we prove that if the manifold under consideration is an immersed submanifold of the vector space, considered as ambient manifold, then it is possible to construct explicitly a reduced-order vector field over this submanifold. In particular, we found that the reduced-order vector field satisfies the variational principle of Dirac–Frenkel and that we can formulate the Proper Orthogonal Decomposition under this framework. Finally, we propose a local-point estimator of the time-dependent error between the original vector field and the reduced-order one.     

力矩析微

力矩是力学教学中最重要的基础概念之一,但教材中一般会同时给出力对点之矩和力对轴之矩两种定义,这在概念上容易引起学习者的困惑,尤其是空间问题中的力对点之矩,从物理意义的角度讲更是不易理解.本文在利用杠杆原理阐述力矩定义起源的基础上明确指出:力矩本质上即力对轴之矩,是力使刚体绕特定轴转动效应的一种度量,是滑动矢量;而力对点之矩是力对轴之矩的一种抽象的等价表述,是定位矢量,是力矩概念在复杂应用中的进一步发展.这种解释理清了力对点之矩与力对轴之矩两种定义之间的关系,物理意义明确直观,更有利于教学和实践中对力矩概念的清晰理解和准确应用.     

Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.

     

Correction to: Fast data-driven model reduction for nonlinear dynamical systems

Nonlinear Dynamics -     

A new model reduction method for nonlinear dynamical systems

The present research work proposes a new systematic approach to the problem of model-reduction for nonlinear dynamical systems. The formulation of the problem is conveniently realized through a system of singular first-order quasi-linear invariance partial differential equations (PDEs), and a rather general explicit set of conditions for solvability is derived. In particular, within the class of analytic solutions, the aforementioned set of conditions guarantees the existence and uniqueness of a locally analytic solution. The solution to the above system of singular PDEs is then proven to represent the slow invariant manifold of the nonlinear dynamical system under consideration exponentially attracting all dynamic trajectories. As a result, an exact reduced-order model for the nonlinear system dynamics is obtained through the restriction of the original system dynamics on the aforementioned slow manifold. The local analyticity property of the solution’s graph that corresponds to the system’s slow manifold enables the development of a series solution method, which allows the polynomial approximation of the system dynamics on the slow manifold up to the desired degree of accuracy and can be easily implemented with the aid of a symbolic software package such as MAPLE. Finally, the proposed approach and method is evaluated through an illustrative biological reactor example.     

Dynamic analysis: a new point of view

In this article, an alternative to the classical dynamic equation formulation is presented. To achieve this goal, we need to derive the reciprocal theorem in rates and the principle of virtual work in rates, in a small deformation regime, with which we will be able to obtain an expression for damping force. In this new formulation, some terms that are not commonly considered in the classical formulation appear, e.g., the term that is function of jerk (the rate of change of acceleration). Moreover, in this formulation the term that characterizes material nonlinearity, in dynamic analysis, appears naturally.     

点的复合运动中相对运动的描述

给出了点的复合运动中,动点的绝对运动方程和相对运动方程之间关系的描述方法,并将其应用于确定平面运动机构中选取不同动点和动系时的相对运动轨迹.该方法的推导过程简单易懂,易于实现,可以帮助学生在学习相关知识时对不同情况下的相对运动有清晰、直观的了解.特别是当相对运动非常复杂时,可以借助该分析过程给出相对运动轨迹曲线.