Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session J5: Teaching Classical Mechanics and Non-Linear Dynamics: Highlights from a Gordon Conference |
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Sponsoring Units: FEd Chair: Paula Heron, University of Washington Room: LACC 502B |
Tuesday, March 22, 2005 11:15AM - 11:51AM |
J5.00001: What Should Be in an Intermediate Mechanics Text? Invited Speaker: I shall survey the coverage of several popular intermediate mechanics texts --- texts for a typical junior-level course in classical mechanics. I shall then discuss the difficult choices that must be made by the author of such a book and the teacher using it. Should it include Lagrangian mechanics? (My answer is a definitive ``Yes.'') Should it include Hamiltonian mechanics (``Yes,'' but perhaps a little less emphatically.) and if so when? What about chaos theory? Collision theory? Continuum mechanics? And relativity? [Preview Abstract] |
Tuesday, March 22, 2005 11:51AM - 12:27PM |
J5.00002: Laboratory-based nonlinear dynamics course for science and engineering students Invited Speaker: Matthew Moelter We\footnote{Collaborators: N. Sungar, J. P. Sharpe and N. Fleishon (Physics); K. Morrison and J. McDill (Mathematics); R. Schoonover (Chemistry)} describe the implementation of a new laboratory-based interdisciplinary undergraduate course on nonlinear dynamical systems. Geometrical methods and data visualization techniques are especially emphasized. A novel feature of the course is a required laboratory where the students analyze the behavior of a number of dynamical systems. Most of the laboratory experiments can be economically implemented using equipment available in many introductory physics microcomputer-based laboratories. Student response to the course, especially to the laboratory component, has been enthusiastic and positive. [Preview Abstract] |
Tuesday, March 22, 2005 12:27PM - 1:03PM |
J5.00003: Nonlinear Dynamics of Soft-Matter: Continuum Mechanics in the Classroom Invited Speaker: Recent efforts in soft-condensed matter physics has generated a renewed interest in the fundamental physics of continuum systems. There has been a recognition that a wide variety of systems, from glasses to foams to granular material, exhibit similar behavior with regard to their dynamics. Even under conditions of external driving, these systems are often ``jammed''. In other words, they exhibit a solid like response to the external driving. With sufficient driving force, there is a transition to a flowing state as the system ''unjams''. This flowing state is generally comprised of nonlinear rearrangements of particles within the system. The question has been raised as to whether or not this represents a general new state of matter, or if the details of each individual system is relevant. At the same time, the interest in the response of complex fluids, such as foams and granular matter, that are composed of mesoscopic, or even macrosopic, sized ``particles'' (such as sand grains), has raised interesting questions concerning the application of continuum mechanics to these systems. Both the nonlinear response of these materials and the application of continuum mechanics raise fundamental physics questions that are generally not covered in typical undergraduate (or even graduate) curricula. This talk will not only review some of the important questions in this field, but also present suggestions as to its integration into the undergraduate curriculum. [Preview Abstract] |
Tuesday, March 22, 2005 1:03PM - 1:39PM |
J5.00004: Challenges in enhancing student learning in intermediate mechanics: Identifying the need for a tutorial approach to instruction Invited Speaker: One area of ongoing physics education research at Grand Valley State University is to probe the conceptual understanding and reasoning skills of advanced undergraduates as they make the transition from a traditional sequence in introductory calculus-based physics to their first course in upper-level mechanics. [1] The results thus far are consistent with findings from other investigations in upper division courses, which indicate that persistent difficulties with fundamental concepts can hinder meaningful learning of advanced topics. To address this problem, the tutorial approach developed at the University of Washington [2] is being adapted and incorporated into the intermediate mechanics course. Evidence from ungraded quizzes (pretests) and course exams will be presented to illustrate the presence of specific difficulties and the effectiveness of the modified instructional approach. [1] B.S. Ambrose, Am. J. Phys. \textbf{72} (4), 453 -- 459 (2004). [2] L.C. McDermott, P.S. Shaffer, and the Physics Education Group at the University of Washington, \textit{Tutorials in Introductory Physics} (Prentice-Hall, Upper Saddle River, NJ, 2002). [Preview Abstract] |
Tuesday, March 22, 2005 1:39PM - 2:15PM |
J5.00005: Variational Mechanics in One and Two Dimensions Invited Speaker: We develop heuristic derivations of two alternative principles of least action to be introduced early in the undergraduate physics curriculum. A particle moving in one dimension can reverse direction at will if energy conservation is the only criterion. Such arbitrary changes in direction of motion are eliminated by demanding that \textit{abbreviated action}, the area under the momentum\textit{ vs. }position curve in the phase diagram, have the smallest possible value consistent with conservation of energy. Minimizing abbreviated action predicts particle trajectories in two (and three) dimensions and leads to the more powerful principle of least action of Hamilton, which not only generates conservation of energy but also predicts motion even when potential energy changes with time. [Preview Abstract] |
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