Objects in Motion#

Big Ideas#

  • Newton’s second law of motion gives rise to a system of differential equations which models an object in motion.

  • Constitutive laws such as Hooke’s law for springs and Stokes’ law for drag are equations that describe individual components of a mathematical model. Constitutive laws are themselves mathematical models!

  • Any model of a real-world phenomenon will involve many parameters and the nondimensionalization procedure simplifies the model and determines what role the system parameters play.

  • Use SciPy to compute numerical solutions of differential equations. A computational approach to mathematical modelling allows us to easily simulate and visualize models.

Learning Goals#

  • Apply physical laws to construct mathematical models of objects in motion

  • Apply nondimensionalization process and interpret dimensionless parameters

  • Compute numerical solutions of systems of differential equations