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I'm currently brainstorming for my Math AA HL Internal Assessment (a kind of math investigation paper you must elaborate for the IB Diploma) and I've hit a bit of a roadblock. Snowboarding is a hobby I'm incredibly passionate about, and my teacher suggested leveraging this interest for my IA to enhance personal engagement. The idea I've settled on is to calculate the feasibility of a quintuple cork in snowboarding.

This involves considering constant initial conditions such as the snowboarder's mass, the ramp and landing angles, etc. My initial thought was to apply basic kinematics of projectile motion, but I wanted to dive deeper into more complex mathematics. That's where Euler's equations for rigid body dynamics come in, which involve matrices and differential equations of rotation. These equations seem perfect for adding a sophisticated and challenging element to my project.

However, I'm facing a significant hurdle. The research papers and resources I've found on Euler's equations are predominantly collegiate-level. With no prior experience in these types of equations, I'm struggling to grasp the concepts and apply them to my project.

Has anyone here tackled something similar or have experience with Euler's equations in the context of a high school level project? I'm looking for advice or resources that could make these equations more approachable for someone at my level. Any help or guidance would be immensely appreciated.

Link to my original question (I decided to make another post for more visibility, since my other question is already old and doesn't obtain any further answers): Equations modelling a snowboarder/skier on a jump

Miles Jarra Gloekler
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One problem you might have is that Euler's equations relate external torque to angular acceleration and apply to a rigid body. Some of the torque might come from the curved shape of the ramp. But some of it comes from twisting your shoulders and leaning back as you leave. For a quintuple twist, you will need a vigorous twist. Also you control your rate of spin by tucking or moving your arms.

This means you aren't rigid. That isn't fatal. But it means your moment of inertial changes from moment to moment.

All the external torque come from the force of the snow on the board. Once you are airborne, the torques are $0$. This doesn't mean you can't change angular velocity. It means you do so by changing your moment of inertia.

mmesser314
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