Features:

  1. In physics, chaos is a super-sensitivity to initial conditions combined with complex dynamical evolution.

  2. Many physical systems exhibit chaos, but it's NOT so obvious in everyday life.

    Why? Well we don't usually build our machines and other artificial physical systems to exhibit chaos. You wouldn't want your car engine to be chaotic, now would you?

  3. Now as to the animation, you can see the motion (AKA dynamical evolution) is very complex.

    If the initial conditions were changed just a tiny amount, you would also see a complex dynamical evolution, but a very different one.

    So the double pendulum exhibits chaos---but NOT KAOS.

  4. In the double pendulum system of the animation, friction, air drag, and any other forces (like friction inside materials) that dissipate macroscopic mechanical energy (the sum of kinetic energy and gravitational potential energy) to waste heat energy are NOT implemented.

    As a result the motion is perpetual motion which is impossible in reality in the macroscopic world since one can never absolutely turn off all dissipation. One can make it very small in some cases. So the animation represents, an ideal limit that can only be approached, but NOT reached, in the macroscopic world.

    The microscopic world? That takes a bit of a discussion will NOT give here.

    The animation repeats after awhile as one can see. So you do NOT see perpetual motion even though it does exist for this ideal system.

  5. Chaos videos (i.e., Chaos videos):
    1. Chaotic 1,3 pendulum | 40: Here we have a rather complex dynamical system of 3 coupled double pendulums. Though the 3 lower pendulums are nearly identical and their initial conditions are nearly the same, we see that their dynamical evolutions quickly diverge. We have chaos: super-sensitivity to initial conditions combined with complex dynamicsl evolution. Actually, the dynamical evolutions of the 3 lower pendulums are coupled as seen in the video: i.e., they interact and are NOT independent. In this real case of double pendulums, dissipation of mechanical energy due mainly to friction eventually will cause the dynamical system to come to rest with everything just hanging down, and so the dynamical evolutions do eventually converge. This hasn't quite happened by the end of the video. Without friction and other dissipation forces, the dynamical evolutions would probably never converge again, although they would approach convergence from time to time. Short enough for the classroom.
    2. N body simulation in Python with code (precision approach) | 1:01: Good. N-body simulations for N = 3, 4, 13, and 30 point particles calculated using a Python code. Full information is NOT given with the video, but yours truly assumes the particles have equal mass and are point particles (i.e., they have zero size, and so NEVER collide in a body-body sense NOR merge. The initial conditions must chosen in some good fashion for illustrative purposes. Yours truly believes that initial conditions are such the systems are gravitationally bound which is equivalent to saying kinetic energy plus gravitational potential energy sums to less than zero. Being gravitationally bound means that NOT all the point particles can go to infinity relative to each other. Due to complex gravitational interactions (including explicit gravity assists: strong two-body interactions that change orbital trjectories) can eject individual point particles to infinity, but the remaining ones are more tightly gravitationally bound. In some cases depending on initial conditions, so many ejections may occur that only 2 point particles, and they can NEVER escape from each other.
            In the N=4 N-body simulation at t=0:23, there is a gravity assist probably leading to one point particle becoming unbound and going on an escape trajectories to infinity. Of course it is possible the point particle is merely on a very long bound orbit and would return to the other point particles if the N=4 N-body simulation ran longer.
            Another thing to notice is that point particles speed up as they approach each other. This is because their gravitational potential energy (which is greater when they are remoter) turns into kinetic energy as they approach each which is understood by the principle of conservation of mechanical energy.
            Note open star clusters if they are formed bound (and they NOT be) often suffer considerable escape during their existence to internal and external gravitational interactions and disperse in typically a few hundreds of millions of years, a process often called "evaporation" (see Wikipedia: Open cluster: Eventual fate).
            Note also that there are NO exact analytic solutions for 3 or more bodies interacting via gravity. One must solve such systems by perturbation theory or numerical methods (e.g., N-body simulations) on the computer. There is an exact analytic solution for gravitationally bound 2-body system within Newtonian physics.
            Short enough for classroom.
    3. N-Body Chaotic orbit | 0:50: Yours truly will NOT attest to the accuracy of this N-body simulation and it's NOT clear what dynamical system is being simulated. Yours truly guesses the dynamical system is a 3-dimensional system (shown in 2-dimensional projection) of point masses interacting only through gravity and exhibiting chaos. One guess again that the system is a gravitationally-bound system, but due to the chaotic motion some point masses achieve escape velocity it seems.