Investigation
IS A DOUBLE PENDULUM A CHAOTIC SYSTEM?
Hypothesis
If a system that is highly sensitive to initial conditions is dynamic, deterministic, and greatly affected by the starting conditions the system; then the double pendulum, a deterministic and dynamic system, should be highly sensitive to initial starting conditions since its added variables (from the second rod and mass) give the system much more possible states and make its starting conditions very difficult to recreate. The difference between the double pendulums with different initial starting conditions (angles and velocity) should increase as time goes on.
If a chaotic system is characterized by dense periodic orbits, topologically mixing phase space, and high sensitivity to initial starting conditions; and a double pendulum has the first two characteristics and should be highly sensitive to initial starting conditions according to the reasoning above; then a double pendulum should meet all three characteristics and be considered a chaotic system.
If a chaotic system is characterized by dense periodic orbits, topologically mixing phase space, and high sensitivity to initial starting conditions; and a double pendulum has the first two characteristics and should be highly sensitive to initial starting conditions according to the reasoning above; then a double pendulum should meet all three characteristics and be considered a chaotic system.
Variables
Independent Variable: Initial starting conditions (angle or velocity).
Dependent Variable: Path of double pendulum.
Controlled Variables: Method of calculation (computer), application used for animation (Mathematica), application used for tables and line graphs (Excel), numeric values of terms not altered as an initial starting condition (such as rod length and mass weight).
Dependent Variable: Path of double pendulum.
Controlled Variables: Method of calculation (computer), application used for animation (Mathematica), application used for tables and line graphs (Excel), numeric values of terms not altered as an initial starting condition (such as rod length and mass weight).