About the Project
22 Jacobian Elliptic FunctionsApplications22.19 Physical Applications
Figure 22.19.1 (See in context.)
See accompanying text
Figure 22.19.1: Jacobi’s amplitude function am⁡(x,k) for 0≤x≤10⁢π and k=0.5,0.9999,1.0001,2. When k<1, am⁡(x,k) increases monotonically indicating that the motion of the pendulum is unbounded in θ, corresponding to free rotation about the fulcrum; compare Figure 22.16.1. As k→1−, plateaus are seen as the motion approaches the separatrix where θ=n⁢π, n=±1,±2,…, at which points the motion is time independent for k=1. This corresponds to the pendulum being “upside down” at a point of unstable equilibrium. For k>1, the motion is periodic in x, corresponding to bounded oscillatory motion.
© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.0; Release date 2024-03-15.
Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov