Science and computer models
Olis Rubin · 2022
This chapter shows how the motion of physical objects can be modeled by differential equations. It explores how a digital simulation program could produce truncation or roundoff errors. The chapter explains how we can simulate the orbit of a planet around a Sun. It provides case studies that serves as stepping stones that lead to the creation of more complex models that are needed by industry. The gravitational force exerted by the Sun on a planet is equal and opposite to that exerted by the planet on the Sun, so the Sun will also move in a small orbit. The chapter provides a symmetrical situation where a rotation of the pendulum from its lowest position produces a moment that pulls the pendulum back towards the lowest position. Lagrange's equations can be derived from Newton's laws of motion. The chapter illustrates the formal procedure by again deriving the equations of motion for a pendulum.