Elastic pendulum

"Spring pendulum" redirects here. Not to be confused with the one-dimensional vertical spring-mass system with gravity, cf. also Simple harmonic motion#Mass on a spring.

In physics and mathematics, in the area of dynamical systems, an elastic pendulum[1][2] (also called spring pendulum[3][4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system.[2] For specific energy values, the system demonstrates all the hallmarks of chaotic behavior and is sensitive to initial conditions.[2]At very low and very high energy, there also appears to be regular motion. [5]The motion of an elastic pendulum is governed by a set of coupled ordinary differential equations.This behavior suggests a complex interplay between energy states and system dynamics.

  1. ^ Xiao, Qisong; et al. "Dynamics of the Elastic Pendulum" (PDF).
  2. ^ a b c Pokorny, Pavel (2008). "Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum" (PDF). Regular and Chaotic Dynamics. 13 (3): 155–165. Bibcode:2008RCD....13..155P. doi:10.1134/S1560354708030027. S2CID 56090968.
  3. ^ Sivasrinivas, Kolukula. "Spring Pendulum".
  4. ^ Hill, Christian (19 July 2017). "The spring pendulum".
  5. ^ Leah, Ganis. The Swinging Spring: Regular and Chaotic Motion.