In this recipe, we will give an application example of the function minimization algorithms described earlier. We will try to numerically find the equilibrium state of a physical system by minimizing its potential energy.
More specifically, we'll consider a structure made of masses and springs, attached to a vertical wall and subject to gravity. Starting from an initial position, we'll search for the equilibrium configuration where the gravity and elastic forces compensate.
Let's import NumPy, SciPy, and matplotlib:
In [1]: import numpy as np import scipy.optimize as opt import matplotlib.pyplot as plt %matplotlib inlineWe define a few constants in the International System of Units:
In [2]: g = 9.81 # gravity of Earth m = .1 # mass, in kg n = 20 # number of masses e = .1 # initial distance between the masses l = e # relaxed length of...