Bagpipes configurations in mechanics and electromagnetism

✍ Scribed by F.G. Gascon; D. Peralta-Salas

• Book ID: 104045324
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 540 KB
• Volume: 42
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/j.mcm.2005.07.001

✦ Synopsis

It is shown that when a first integral I of a vector field (v.f. in what follows) X is known, the level sets of I resemble bagpipes, and X is asymptotically stable (a.s. in what follows) on the skeleton of I (the set where VI vanishes), then the v.f. is stable at 0 (a singular, not necessarily isolated, zero of X). A similar bagpipes configuration is shown to appear concerning the orbits of the magnetic field created by a set of concurrent straight line wires. (~ 2005 Elsevier Ltd. All rights reserved.