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首页> 外文期刊>International Journal of Mechanical Engineering Education >The moving frame method in dynamics: Reforming a curriculum and assessment
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The moving frame method in dynamics: Reforming a curriculum and assessment

机译：动力学中的移动框架方法：改革课程和评估

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Rigid body dynamics, a gateway course to the mechanical engineering major (and related majors), focuses on a view of motion that is not commensurate with the contemporary age in which mobile devices have on-board inertial firmware. The traditional approach to this topic deploys a mathematical notation, and associated algebra, that inordinately privileges the inertial frames and 2D motion. This limits the study of machines to two-dimensional problems, lends an appearance of whimsy to solutions that obfuscates the theory of motion. We propose a new mathematical approach to dynamics to reinvigorate the discipline and motivate students. The new approach uses modern mathematical tools which have been distilled to tractability: Lie Group Theory, Cartan’s Moving Frames and a new compact notation from Geometrical Physics. The reconstructed course abandons the cross product—a toxic algebraic operation due to its failure to adhere to associativity. We minimize the use of vectors and replace them with rotation matrices. Sophomores learn to solve 3D Dynamics problems with as much ease as solving 2D problems. Typical problems include the precession of tops, gyroscopes, inertial devices to prevent ship roll at sea, and 3D robot and crane kinetics. A critical aspect of this new method is the consistency: the notation is the same for 3D and 2D problems, from advanced robotics to introductory dynamics, students learn the name notational method. The first objective of this paper presents the new mathematical approach to rigid body dynamics—it amounts to an introductory, yet simplified, lecture on a new method. The second objective presents assessment over a three-year period. In the first year, we taught using the old 2D vector-based approach. In the second year, we transitioned to the new method and compared student perceptions in the first two years. In the third year, the course was refined. The goal of this effort is to retain students in mechanical engineering by offering them a new view of the discipline, rather than simple pedagogical course interventions such as e-learning or flipped classrooms. The course content is delivered using the emerging visualization technology: WebGL. WebGL represents the future of the 3D web. It requires no downloads and no plugins. Students are directed to a web site where all images for the lectures are 3D and interactive. The animations run on cell phones, laptops and other mobile devices. It is the contention of this paper that modernizing the math will do more to reduce attrition than learning interventions. This new approach reduces conceptual difficulties that accompany 2D restrictions. It opens many questions on how students perceive 3D space and invites research into how exploiting more modern mathematical math may improve learning.
机译：刚体动力学是通向机械工程专业（及相关专业）的入门课程，着眼于与移动设备具有内置惯性固件的现代时代不相称的运动观。解决该问题的传统方法是使用数学符号和相关的代数，从而惯性地赋予惯性帧和2D运动特权。这将机器的研究限制在二维问题上，使解决运动理论的想法显得古怪。我们提出了一种新的动力学数学方法，以重振学科并激发学生的积极性。新方法使用了已提炼为易处理性的现代数学工具：李群理论，Cartan的移动框架和来自几何物理的新紧凑表示法。重建的过程放弃了叉积-由于无法遵守关联性，因此是有毒的代数运算。我们将向量的使用降到最低，并用旋转矩阵替换它们。大二学生学会解决3D动力学问题就像解决2D问题一样容易。典型的问题包括顶部，陀螺仪，防止船舶在海上滚动的惯性装置的进动，以及3D机器人和起重机的动力学。这种新方法的一个关键方面是一致性：对于3D和2D问题，表示法是相同的，从高级机器人技术到入门级动力学，学生都可以学习名称表示法。本文的第一个目标是提出一种刚体动力学的新数学方法，相当于对一种新方法进行了介绍性但简单的讲授。第二个目标是对三年期的评估。在第一年，我们使用旧的基于2D矢量的方法进行教学。在第二年，我们过渡到了新方法，并比较了前两年的学生看法。第三年，课程进行了完善。这项工作的目的是通过向学生提供该学科的新视角来留住机械工程专业，而不是像电子学习或翻转教室这样的简单教学课程干预措施。使用新兴的可视化技术WebGL交付课程内容。 WebGL代表3D网络的未来。它不需要下载，也不需要插件。将学生定向到一个网站，该网站的所有演讲图像均为3D交互式图像。动画在手机，笔记本电脑和其他移动设备上运行。本文的论点是，与学习干预相比，现代化数学将在减少损耗方面做更多的事情。这种新方法减少了2D限制带来的概念上的困难。它提出了许多有关学生如何看待3D空间的问题，并邀请人们研究如何利用更现代的数学来改善学习。

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