双摆系统运动理论与实验研究.pdf

The Chaotic Motion of a Double Pendulum Carl W. Akerlof April 12, 2010 The following notes describe the kinematics of the double pendulum. The starting point is a pendulum consisting of two point masses, m, and m , suspended by massless wires of length l 2 1 and l . The treatment of this case can be found at: 2 /physics/DoublePendulum.html For a real system, the equations of motion depend in a more complicated way on the distribution of mass that is essential for modeling the physical pendulum used in this experiment. Figure 1. Point mass double pendulum. Figure 2. Extended mass double pendulum. University of Michigan 1 Department of Physics Double pendulum with point masses: x l sin  1 1 1 y l cos  1 1 1 x l sinl sin  2 1 2 2 y l cos  l cos  2 1 1 2 2   x l cos   1 1 1 1   y l sin   1 1 1 1    x l l cos    cos   2 1 1 1 2 2 2    y l sin   l sin   2 1 1 1 2 2 2 2 2 2   r l 