Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Relaxed stability Relaxed stability In aviation, relaxed stability is the tendency of an aircraft to change its attitude and angle of bank spontaneously. An aircraft with relaxed stability will oscillate in simple harmonic motion around a particular attitude at an increasing amplitude. This can be contrasted with the behaviour of an aircraft with positive stability, which, when trimmed to fly at a certain attitude, will continue to do so in the absence of control input, and if perturbed will oscillate in simple harmonic motion on a decreasing scale around and eventually return to the trimmed attitude. A positively stable aircraft will also