Using Differential-Algebraic Equations to Model Classical Mechanics
0Day 1 | 8:00 PM–8:30 PM
"Using Differential-Algebraic Equations to Model Classical Mechanics"
Presented by:
Joseph Eichholz, United States Air Force Academy, USAFA CO USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: Though modeling has taken an increasingly prominent role in the undergraduate ODE curriculum, the classical mechanics introduced in such courses is often limited to basic problems like mass-spring systems or pendulums. This is likely due to the complexity of deriving equations of motion for more advanced mechanics problems, requiring either heavy algebra or a switch to Lagrangian or Hamiltonian mechanics, or both. This talk presents a coherent framework, suitable for undergraduates in an ODE course, for deriving differential-algebraic equations (DAE) of rigid-body motion using Newtonian mechanics, converting DAE to pure ODE, and solving them. We also introduce MATLAB tools for analytical and numerical solutions, enabling the analysis of complex rigid-body motion beyond typical undergraduate coursework. The goal of the project is to provide a toolbox with which undergraduates can readily model motion of complex systems well beyond the scope of the typical ODE course