Over the Christmas break, my maths teacher told us to come up with a "plan of attack" for our maths explorations. Our entire class isn't quite sure what that means so we're all at different stages of it. I was hoping to get some help with a few ideas that I have.
1. The Brachistochrone problem - I'm really interested in this problem but the problem I have with it is that I'm not sure if it is way out of the scope of the maths SL syllabus. All the IA's I've seen on this topic have been from HL so I know it isn't overdone but this has led me to wonder whether this lack of SL IAs on this topic is for a reason. From what I've seen this is primarily a question of calculus of variations and optimisation.
For anyone who doesn't know, the brachistochrone problem was put forward by Johanne Bernoulli in 1696 and the problem goes like this: given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and ends at B in the shortest time.
2. Minimising the drag force on a spacecraft - I have a lot of information on this but I haven't been able to find much specifically for IB maths. There is a bunch of stuff from NASA about this and I believe this is a question of calculus as well.
Pretty sure I would go about this by finding the optimal size of a rocket to allow it to be as light as possible while carrying the most payload. When putting it like that it feels a bit simple.
3. Finding the optimal orbital transfer - I know the optimal orbital transfer is a Hohmann transfer but I've always been interested in space flight and thought it would be cool to work my way there. This is also a question of calculus of variations I believe and I haven't been able to find much in terms of this for IB maths.
4. Looking at Kepler's First and Second Laws - I know a bit about this from personal research and think it is really interesting. I was thinking of creating a star system with a planet orbiting around it, and then looking at how distance from the star affects the speed of said planet. I could using differentiation to see the relationship of this but other than that not really sure what else I could do.
Any input is greatly appreciated, please let me know your thoughts on these.