Mathematica Catapult Dynamics Modeling
Budget: €8 – €30 EUR
I have to hand in a university assignment that centres on the dynamic modelling and mechanical synthesis of a small catapult. Your job is to build the full dynamic model in Wolfram Mathematica, starting from first principles with Lagrange methods, and drive it all the way to an optimisation that shows which geometric or mass parameters deliver the longest range.
I will share a previously solved, very similar exercise so you can lean on its structure, but the final notebook and exposition must be entirely original and ready for submission. The budget for the whole task is capped at about €30, so a concise, well-commented solution is exactly what I am after rather than an over-engineered one.
Core objectives
• Derive the equations of motion with the Lagrangian approach.
• Implement them in a clean, reproducible Mathematica notebook.
• Simulate the projectile’s flight, extract range, and plot key responses (angular displacements, velocities).
• Identify the key design variables (arm length, counterweight, pivot position, etc.) and perform an optimisation sweep that clearly points out the configuration yielding maximum range.
Acceptance criteria
1. Notebook runs end-to-end in the latest public release of Wolfram Mathematica without additional packages.
2. Code sections are commented so a mechanical-engineering student can follow each step.
3. Optimised range result is repeatable by re-executing the notebook.
I will share a previously solved, very similar exercise so you can lean on its structure, but the final notebook and exposition must be entirely original and ready for submission. The budget for the whole task is capped at about €30, so a concise, well-commented solution is exactly what I am after rather than an over-engineered one.
Core objectives
• Derive the equations of motion with the Lagrangian approach.
• Implement them in a clean, reproducible Mathematica notebook.
• Simulate the projectile’s flight, extract range, and plot key responses (angular displacements, velocities).
• Identify the key design variables (arm length, counterweight, pivot position, etc.) and perform an optimisation sweep that clearly points out the configuration yielding maximum range.
Acceptance criteria
1. Notebook runs end-to-end in the latest public release of Wolfram Mathematica without additional packages.
2. Code sections are commented so a mechanical-engineering student can follow each step.
3. Optimised range result is repeatable by re-executing the notebook.