So here we have the V Python, Focult's Pendulum Program for this class. So we're just going to go and run it, just show that it works out here real quick. So in this view here, we see the pendulum running on an Earth, or some planet with a day that lasts about 1000 seconds. The pendulum is 1 meter long, and is a period of approximately 2 seconds. The path has been drawn out for about one revolution, so that we see our one revolution of the pendulum. So we see that whole trail as it goes along. And then also on the graph, we see a plot of the position, the exposition versus the Y position, a parametric plot, to show us the position of the pendulum relative to the rotating reference frame. So now if we look at the code, we can see that we've created a simple pendulum with some initial values for its mass, its angular momentum, angular momentum, and rotational inertia. And furthermore, we set an initial force of gravity, and we set that the torque on the pendulum is going to be equal to the cross product of the ball's position and the force of gravity. We have a time step set at 100th of a second, and we have our loop that is going to animate the pendulum, running 100 times a second from the rate statement here. Beginning in the loop, we start by re-evaluating the torque on the pendulum by taking another cross product for the ball's position and the force of gravity. Then we implement angular momentum principle to update the angular momentum ball.l, and then furthermore, use that to update the angular position of the end of the pendulum. Then using our pole to our pole to cart function, which I created up at the top, to convert from polar to Cartesian coordinates, we take our angular position to get an XYZ vector position to animate the position of the ball. Then furthermore, we create the string by just telling it what the string is, is a vector from the origin, which is the axis of rotation of the pendulum to the ball's position. Next with this statement, we tow it to a panda trail to the end of the pendulum, well, t is less than 6 seconds so that we see the motion of the pendulum relative to the rotating reference frame. Next in the loop, we have this pegs dot rotate statement, where we begin to rotate the reference frame, just as the earth rotates under a full-cult pendulum to prove that the earth, in fact, rotates. So that's rotating our pegs the earth, and then down here with our beta equals beta plus lat tang, lat function as well as the scene dot forward, we're rearranging the camera so that it rotates at the same angular velocity as the pegs do. So by rotating a camera and the earth that the pendulum is rotating with, or isn't rotating with reference to, you know what I'm trying to say, we see that it actually looks as a focal-cult pendulum wood on the earth. Furthermore, this is just our graph for the position, and we actually had to come up with this little trick where we took the ball's x position multiplied by a cosine of beta to find the x position relative to the rotating reference frame, where beta is the angle that the reference frame has rotated from its initial position for the x position, relative to the reference frame, and then for the y position relative to the reference frame, we would multiply the ball position in the x direction times the sine of beta once again, that angle that the reference frame has rotated to find the y position relative to the moving reference frame. So now then we're actually going to talk a little bit about what kind of things we can modify here. So up here with this latitude are lat. We have equal to the latitude of the pendulum where it is on the earth. So at the moment we have it at pi over 2 or 90 degrees, which would mean that the pendulum is at the north pole of whatever planet we are on. So it's at the tip of the axis of rotation. So that means we have maximum rotational effects due to the rotation. However, for example, if we were to put the pendulum at zero degrees or the equator, while we would see that we don't have any rotational effects, and this just acts like a regular pendulum. We just see the pendulum go back and forth with that path maintaining just what we'd expect from a regular pendulum, and on the position we just see that the pendulum goes back and forth in the x direction, with no change in the y direction. If we were to put it anywhere in between, we just see the same similar effects, just somewhere in between no effects, and the full effects that we see at 90 degrees. We can use it with that, although they said that, it's a request to set, and they want that. So something that was going to allow us to have a couple of measures for the non-direct state. But I don't want to do it this year, but I think that's a good idea. Sorry about that. I'm pi over 2. For them, we could change the acceleration due to gravity, so act like we're on another planet, we could change the length of the pendulum, or we can change the length of the day. So to create something that would behave similarly to an Earth Day, we're going to have 100,000 second long day. So that's 100,000 seconds, and we're going to try running that to see how it would behave as if it were on Earth, and at the Earth's North Pole. We see that the petals of the flower created a much spaced, much more closely together, the effects are much more limited, because the Earth's Day is extremely, or the Earth's rotation is much slower compared to the period of the pendulum. However, when I was at 1,000 seconds before, we saw that nice petal action getting about six petals, to create that very obvious, full-culted pendulum effect. However, if we create an Earth Day, or a day of only 100 seconds, we see some more interesting effects, where the graph behaves quite strangely. Initially, I suspected that this might be because the length of the day was longer, sorry, the length of the day was shorter than the period with the pendulum, but in fact, that's not the case, because here the day is 100 seconds long, and the period of the pendulum is two seconds, but we still get this very weird behavior, because it appears as if it's doubling back retrograde motion, similar to what the planets undergo, when they pass each other, or relative to Earth. This was a problem. This was one of many problems with a geocentric model, because we would see planets start to do loops, Mars in particular, was the one that, earlier astronomers noted for this strange retrograde motion. If we said it that the length of the day is in fact equal to the period of the pendulum, we get some crazy effects, probably just because of the limits of the Python, and so it's just overall craziness, really, so that doesn't really matter. So I'll put that back up to 1000, and I guess I can show you the pedal effects that we were, oh, actually one more thing. Up here we have this function that I've defined, lacting a phi, where phi is the argument of the function, and all that this means is we can take the latitude in this case, which I'm seeing is phi. I take the sign of that multiply to pi, and then divide by the length of the day, and what that gets us is the angular velocity of the Earth's rotation and that current location, so that helps us measure the effects, or the full-cult effects. So I guess I'll just show you a good example with six pedals with a thousand second long day, and that'll be it. So actually, and sorry, let me correct there, it's a five-pedal effect with a hundred second long day, I was saying a six-pedal effect before, but it's actually only five pedals, so that'll be all for now. Thank you for listening.