Gastvortrag 22.05.2018 – 16.00 – Raum M 0526
„The Shoelace Catastrophe (or a Knotty Problem on a Shoestring)“
Dozent: Professor Oliver M. O’Reilly, University of California at Berkeley
The accidental untying of a shoelace while walking often occurs without warning. Modeling and simulating the untying is an exceptionally difficult task in part because of the wide range of length scales, time scales and parameters. Finding external funding to examine the problem is arguably an even harder problem.
In this talk, we present a set of hypotheses for the series of events that lead to a shoelace knot becoming untied. First, the repeated impact of the shoe on the floor during walking serves to loosen the knot. Then, the whipping motions of the free ends of the laces caused by the leg swing produce slipping of the laces. This leads to eventual runaway untangling of the knot. As demonstrated using slow-motion video footage and a series of experiments, the failure of the knot happens in a matter of seconds, often without warning, and is catastrophic. The controlled experiments showed that increasing inertial effects of the swinging laces leads to increased rate of knot untying, that the directions of the impact and swing influence the rate of failure, and that the knot structure has a profound influence on a knot’s tendency to untie under cyclic impact loading. The research was conducted over a period of three years on weekends and spare time using borrow equipment and laboratory space.
This talk is based on a paper, coauthored with Christopher Daily-Diamond and Christine Gregg, published last year in the Proceedings of the Royal Society: http://bit.ly/KnotFailing which captured widespread media attention.
Gastvortrag 23.05.2018 – 14.00 – Raum M 0526
„A New Geometric Explanation for Gimbal Lock in the Apollo Moon Landing Program and Related Problems“
Professor Oliver M. O’Reilly, Dozent University of California at Berkeley
Coordinate singularities and gimbal lock are two phenomena that present themselves in models for the dynamics of mechanical systems. The former phenomenon pertains to the coordinates used to parameterize the configuration manifold of the system, while the latter phenomenon has a distinctive physical manifestation and rose to prominence in the Apollo Moon landing program. In the Apollo program a platform was mounted on two gimbals to save weight but this lead to locking of the gimbals and failure of the platform as a navigation aid in certain circumstances. To avoid locking, three gimbals could be used but this option was discarded in the interests of conserving weight. In this talk, we use tools from differential geometry to show how gimbal lock is intimately associated with an orthogonality condition on the applied forces and moments which act on the system. This condition is equivalent to a generalized applied force being normal to the configuration manifold of the system. Numerous examples, including the classic bead on a rotating hoop example and a gimbaled rigid body, are used to illuminate the orthogonality condition. These examples help to offer a new explanation for the elimination of gimbal lock by the addition of gimbals and demonstrate how integrable constraints alter the configuration manifold and may consequently eliminate coordinate singularities. This talk is based on the recent paper in Multibody System Dynamics coauthored with Evan Hemingway: doi.org/10.1007/s11044-018-9620-0
— Prof. Dr.-Ing. Robert Seifried Institute of Mechanics and Ocean Engineering Hamburg University of Technology (TUHH) Eißendorfer Straße 42, room 0511/0512 21073 Hamburg, Germany