{"id":775,"date":"2019-11-26T23:52:34","date_gmt":"2019-11-26T21:52:34","guid":{"rendered":"http:\/\/www.joanillo.org\/?p=775"},"modified":"2020-10-05T23:55:00","modified_gmt":"2020-10-05T21:55:00","slug":"llibre-elementary-mechanics-using-python","status":"publish","type":"post","link":"https:\/\/www.joanillo.org\/?p=775","title":{"rendered":"Llibre: Elementary Mechanics Using Python"},"content":{"rendered":"

\"\"<\/a>Tinc un nou repte pel que queda de 2019 i per al primer semestre del 2020. He comen\u00e7at a llegir el llibre Elementary Mechanics Using Python: A Modern Course Combining Analytical and Numerical Techniques<\/strong><\/em>, de Anders Malthe-S\u00f8renssen<\/em>. \u00c9s tot un curs de f\u00edsica, i combina de manera bastant entenedora els exemples cl\u00e0ssics de moviment, forces, energia,… amb les seves solucions num\u00e8riques, utilitzant les llibreries matem\u00e0tiques i de fer gr\u00e0fiques de Python.<\/p>\n

Es tracta d’implementar tots els exemples del llibre a codi Python. No he vist cap enlla\u00e7 per descarregar tot el codi, en qualsevol cas, els exemples vull adaptar-los i fer-me’ls meus. He comen\u00e7at per l’exemple del pes susp\u00e8s d’una molla, que com tothom sap la soluci\u00f3 del moviment \u00e9s sinusoidal al voltant del punt d’equilibri, la velocitat \u00e9s zero en els punts m\u00e0xim i m\u00ednim, i la velocitat \u00e9s m\u00e0xima en el punt d’equilibri. Aquest exemple s’explica en l’apartat 5.7, que parla de forces, i no n’hi ha prou en copiar i enganxar el codi, sin\u00f3 que l’he hagut d’adaptar. Aquesta \u00e9s la meva soluci\u00f3:<\/p>\n

\n# -*- coding: utf-8 -*-
\nimport matplotlib.pyplot as plt
\nimport numpy as np<\/p>\n

# Initialize
\nm = 1.0
\n# kg
\nk = 100.0 # N\/m
\nv0 = 1.0
\n# in m\/s
\ntime = 2.0 # s
\ng = 9.8 # m\/s^2<\/p>\n

# Numerical setup
\ndt = 0.0001 # s
\nn = int(round(time\/dt))
\nt = np.zeros(n,float)
\ny = np.zeros(n,float)
\nv = np.zeros(n,float)
\n# Initial values
\ny[0] = 0.0
\nv[0] = v0
\n# Simulation loop
\nfor i in range(n-1):
\n\\tF = -k*y[i] – m*g
\n\\ta = F\/m
\n\\tv[i+1] = v[i] + a*dt
\n\\ty[i+1] = y[i] + v[i+1]*dt
\n\\tt[i+1] = t[i] + dt<\/p>\n

fig = plt.figure()
\nfig.suptitle(u”Objecte susp\u00e8s d’una molla”)
\nplot1 = fig.add_subplot(211)
\n#plot1.set_xlabel(‘t [s]’)
\nplot1.set_ylabel(‘y [m]’)
\nplot1.xaxis.grid()
\nplot1.plot(t,y)
\nplot2 = fig.add_subplot(212)
\nplot2.set_xlabel(‘t [s]’)
\nplot2.set_ylabel(‘v [m\/s]’)
\n#plot1.grid(axis=’y’)
\n#plt.grid(b=True, which=’minor’, color=’#666666′, linestyle=’-‘)
\nplot2.xaxis.grid()
\nplot2.plot(t,v)<\/p>\n

for i in range(10, n-1, 400):
\n\\tplot1.plot(t[i],y[i],’ob’)
\n\\tplot2.plot(t[i],v[i],’ob’)<\/p>\n

plt.show()<\/p><\/blockquote>\n

Aquests s\u00f3n els cap\u00edtols i temes que es tracten en el llibre:<\/p>\n

\n4. Motion in One Dimension .
\n5. Forces in One Dimension .
\n6. Motion in Two and Three Dimensions
\n7. Forces in Two and Three Dimensions
\n8. Constrained Motion
\n9. Forces and Constrained Motion
\n10. Work
\n11. Energy
\n12. Momentum, Impulse, and Collisions
\n13. Multiparticle Systems
\n14. Rotational Motion
\n15. Rotation of Rigid Bodies
\n16. Dynamics of Rigid Bodies<\/p><\/blockquote>\n