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 . 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. By: . Nahdir. Austin . Honors Physics. Period 2 . History of the . Pendelum. First used in the . H. an dynasty’s seismometer device by scientists Zhang . Heng. .. T. enth century Egyptian astronomer Ibn Yunis used a pendulum for time measurement.. General Physics. Periodic Motion. A . motion . that is regular and repeating. Examples. Circular motion. Mass bouncing up and down on a spring . Pendulums. Simple Harmonic Motion (SHM). motion that returns an object to its rest position. 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) . m. hanging from a light (massless) string of length . L. . The pendulum undergoes small oscillations, and can be considered to be undergoing simple harmonic motion. If the mass of the point mass is changed to 4. Chapter 1. . Physics Paper B. . BSc. . I. Motion of a body. PERIODIC MOTION- . The motion which repeats itself at a regular intervals of time is known as Periodic Motion. . . 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. Resonance. The pendulum. Springs. Harmonic motion. Mechanical waves. Sound waves. Musical instruments. Tacoma Narrows Bridge. November 7, 1940. http://www.youtube.com/watch?v=xox9BVSu7Ok. 1. Flow past an object. 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.. 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. . Strategic Assessment. Using assessment tools involves three . stages: . Clarifying . the . elements of the targeted performance expectation, . Designing assessment . tasks that are precisely aligned to the specific . 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. © 2016 Pearson Education Inc.. Learning Goals for Chapter 14. D. escribe oscillations in terms of . amplitude. , . period. , . frequency. , & . angular frequency. .. A. pply . simple. . harmonic.