BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mark Blyth (UEA) DTSTART:20260428T120000Z DTEND:20260428T130000Z DTSTAMP:20260423T022803Z UID:UEA_mth/26 DESCRIPTION:Title: Kuzmak’s method - tour de force or tour de farce?\nby Mark Blyth (U EA) as part of Fluids and Structures Seminar @ UEA\n\nLecture held in SCI 3.05.\n\nAbstract\nIn 1959 Kuzmak introduced a new method for constructing asymptotic solutions to ordinary differential equations that describe non linear oscillators. The approach is effectively a nonlinear variant of the WKB method. Kuzmak's method was later refined by Luke (1966) and can be v iewed as a precursor to Whitham Modulation Theory for nonlinear waves. The method appears to be not so well known. In this talk we will show how it can be applied using the example of the simple\, damped pendulum. As is w ell known\, with no damping the problem can be solved exactly using ellipt ic functions\, and the oscillation period depends on the amplitude (i.e. t he oscillations are non-isochronous). With damping active\, the basic asym ptotic approach is one of multiple scales\, with the fast time scale descr ibing the oscillations and the slow time scale describing the gradual dimi nution in amplitude as energy slowly leaks away. In a key step\, the fast time scale is chosen to effectively fix the oscillation period\, and this allows a bounded solution to be constructed. We show how the key elements of the method work\, providing sufficient details to fully construct the l eading order solution.\n LOCATION:https://researchseminars.org/talk/UEA_mth/26/ END:VEVENT END:VCALENDAR