PPT-Chaotic motion in the double pendulum

Dan Hampton and Wolfgang Christian Abstract The double pendulum provides an ideal system in which to study chaotic motion The system is relatively simple but an infinitesimally small change in the initial conditions of the pendulum produces a drastically different trajectory for energies that exhibit chaotic motion I use a phasespace plot a Poincaré section and a 3D trace to graphically represent the pendulums motion The simulation allows for the initial energy and the masses on each pendulum to vary The Feldberg eighth order numerical method serves as the algorithm for computing the motion The program shows the energies at which the motion becomes chaotic while sometimes still exhibiting quasiperiodic trajectories and it quantitatively demonstrates the unpredictability of this simple system . Determinism and Randomness . Classical physics is deterministic!. If you know where you started you know where you are going. Randomness:. Quantum randomness is truly random and unpredictable. A lot of randomness is actually complexity and uncertainty. Clint . Sprott. Department of Physics. University of Wisconsin - Madison. Presented . to Physics 311. at University of Wisconsin. in . Madison, . WI . on . October . 31, 2014. Abbreviated History. Kepler. Pendulums. Gizmo – Energy of a Pendulum. Complete Pendulum handout. Pendulums. What affects the period of a pendulum?. Pendulums. How does the kinetic energy and Potential energy relate to the motion of a pendulum?. What is the motion simple pendulum called? . Starter. Look at the pendulum and describe its motion. . Too Easy? What is the time period of a simple pendulum? . Lesson 10/21. Pendulums oscillate (move side to side) . Limit cycle in phase space: no sensitivity to initial conditions. Pendulum with friction. Fixed point attractor in phase . space: no sensitivity to initial conditions. Pendulum with friction: basin of attraction. University of Michigan. Physics Department. Mechanics and Sound . Intro . Labs. Simple Harmonic Motion. This week you move away from rotational motion and begin to study simple harmonic motion. We say that you move away from rotational motion only in the sense that you will not be studying rotating objects as the main focus of the lab. However, it is worth noting that several concepts from rotational motion can be related to simple harmonic motion. You will study three simple harmonic oscillators today: the mass and spring system, the simple pendulum, and the ball and dish oscillator.. Transport. from a "Ruffled" Separatrix. Axial trapping separatrices are ubiquitous in plasmas, and. traditional Neo-Classical Transport theory calculates. transport effects from . collisional. separatrix crossings.. Zhumagali Shomanov, Evangelos Mitsokapas,. Shirali Kadyrov, Anastasios Bountis. Overview. An introduction to the Standard Map. The transition from regular to chaotic motion. Box counting dimensions and q-Gaussian distributions. Resonance. The pendulum. Springs. Harmonic motion. Mechanical waves. Sound waves. Musical instruments. Tacoma Narrows Bridge. November 7, 1940. https://www.youtube.com/watch?v=nFzu6CNtqec. 1. Tacoma Narrows Bridge Collapse. Period of a Pendulum: . Period based on length (L) and value of gravity (g). Uses/Applications: . Use the . magnitude. of gravity (9.8 m/s. 2. ). Example . 8. A mass (m = 5.67 kg) is attached to a rope with a length of 0.950 m. . MATH441: Spring 2017. R. ö. ssler systems were introduced in the 1970s by Otto Rössler as prototype equations with the minimum ingredients for continuous-time chaos.. The minimal dimensions for chaos is three so R. Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.. Calculate the spring force using Hooke’s law.. OBJECTIVES. What is periodic motion?. A repeated motion (e.g. pendulum swinging) that is back and forth over the same path.. © 2016 Pearson Education Inc.. Learning Goals for Chapter 14. D. escribe oscillations in terms of . amplitude. , . period. , . frequency. , & . angular frequency. .. A. pply . simple. . harmonic. La gamme de thé MORPHEE vise toute générations recherchant le sommeil paisible tant désiré et non procuré par tout types de médicaments. Essentiellement composé de feuille de morphine, ce thé vous assurera d’un rétablissement digne d’un voyage sur .