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指出理论力学教材用几何法证明速度合成定理时存在的错误,从概念和几何两方面给予分析.提出了合理的位移分解图. 相似文献
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本文就运动学中点的合成运动分析方法进行了梳理与研讨。采用广义坐标方法推导了动参考系作一般运动下点的速度与加速度合成公式,并与教材中的表达式进行了对比。此外还采用本文提出的基于牵连点运动的分析方法,对点的合成运动进行了详细的研究,并重点讨论了两种分析方法的特点与应用。
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理论力学是大学工科各专业本科生的技术基础课,点的合成运动是重点与难点内容之一。部分学生对牵连(加)速度,特别是对(加)速度合成定理的推导需要较长时间才能理解和适应。很多教材(如文献[1,2])都引入了“牵连点”的概念。牵连点的定义为:某瞬时与动点重合的动系上的点称为动点在该瞬时的牵连点。由于动点相对动系有运动,不同的瞬时动点与动系上不同的点重合,因此不同瞬时的牵连点是不同的。某瞬时的牵连(加)速度就是该瞬时的牵连点相对定系的(加)速度。牵连点的引入能较好地帮助学生理解牵连(加)速度。在定理推导的教学实践中,虽然用目前的教材中所采用的方法都能很好地证明该定理,但我们注意到,“两点”(即牵连点与动点)在时间点和空间位置上的“重叠性”会给学生带来理解和掌握的难度,学生容易在“重叠性”这一点上产生困惑。文献[3]就动系做定轴转动,采用了一种将动点从其重合点“拉开”的方式,对该定理进行了推导,对解决学生的困惑有一定帮助。以下,本文以文献[3]的方法为基础,补充引入“牵连点”、“绝对和相对导数”等重要概念,并就动系做一般运动对该定理进行推导,在表达方式上也做了一些调整。本文称这种推导方式为“牵连点跟踪法”。 相似文献
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一些经典的工科《弹性力学》教材推导平衡微分方程的过程在数学上不够严密. 利用多元函数偏导数的定义和积分中值定理给出了逻辑严密的推导. 相似文献
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对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正
确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、
自由与约束的关系并得以下结论:
(1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而
异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理.
讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义. 相似文献
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Tibor Javor 《Experimental Mechanics》1968,8(4):171-176
The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect. 相似文献
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It is well known that the problem on nonseparating potential flow of an incompressible fluid about an array of profiles reduces to an integral equation for a certain real function, determined on the contours of the profiles of the array. As such a function one can take, as was done, for instance, in [1–5], the relative velocity of the fluid on the profiles of the array. For arrays of profiles of arbitrary shape it is necessary to solve the corresponding integral equation numerically. In the particular examples of the calculation of aerodynamic arrays that are available [1–3] the numerical methods used were based on the approximate evaluation of contour integrals by rectangle formulas. As investigations showed, sizeable errors arose thereby in the approximate solution obtained, these being especially significant in the case of curved profiles of relatively small bulk. In the present paper a method for the numerical solution of the integral equation obtained in [5] is proposed. The method is based on the replacement of a profile of the array with an inscribed N polygon, the length of whose sides is of the order N–1 and whose internal angles are close to . Convergence with increasing N of the numerical solution to an exact solution of the integral equations at the reference points is demonstrated. Examples of the calculation are given.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–112, March–April, 1972. 相似文献
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