Engineer Essay

535 Words3 Pages
Chaos theory is a study in the field of mathematics, having many applications in sciences such as physics, economics, engineering and many more. The study of chaos theory involves systems that are highly sensitive to initial conditions, also referred to as the butterfly effect. (Chaos Theory) One of the earliest and very famous examples of chaotic studying is the Lorenz attractor, studied by Ed. N. Lorenz in 1963. Lorenz modeled the motion of fluid due to the temperature distribution in the atmosphere. Lorenz found that for weather prediction and modeling, on ten-thousandths digit value could affect the system greatly. (The Lorenz Attractor in 3D) Many studies relating to chaos research was inspired by physics. Birkhoff studied the three-body problem (George D. Birkhoff, 1927). Kolmogorov studied turbulence and astronomical problems (Kolmogorov, A. N., 1954). Cartwright and Littlewood studied radio engineering (Cartwright and Littlewood, 1945). An example of a chaotic motion is the double pendulum that is strongly sensitive to initial conditions. The double pendulum consists of two pendulums attached to each other and it’s an example of a physical system that shows a dynamic behavior with sensitivity to initial conditions (Double Pendulum). The system is a two dimensional one with two degrees of freedom and is shown in the following figure: Double pendulums are commonly used in seismic resistance designs in building and earthquake engineering for gravitational wave detection. It is important to model the motion of a double pendulum which gives a real life simulation of the motion and helps in predicting its behavior. To simulate the motion of a double pendulum, it’s equations of motion has to be developed and solved. The equations of a double pendulum must be solved using numerical methods since solving it analytically will be very complicated. Numerical