File:Centripetal force vs external force vectors.svg
| Uploaded by | Svebert |
|---|---|
| Upload date | 2013-02-28T17:58:45Z |
| MIME type | image/svg+xml |
| Dimensions | 623 × 327 px |
| File size | 233.6 KB |
Summary
| Description |
English: Shows in the upper half the position of a valve of a wheel seen from the reference frame ”Street” -> Cycloid
Lower part: The decomposition of the external force (left side of newton 2)
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| Date | |
| Source | Own work |
| Author | Svebert |
| SVG development |  This plot was created with Matplotlib. |
| Source code | Python code############Script to produce this figure (python)##############
from math import *
import numpy as np
import matplotlib.pyplot as plt
tarr=np.linspace(-1.0,3*pi,400)
xarr=np.zeros(len(tarr))
yarr=np.zeros(len(tarr))
vxarr=np.zeros(len(tarr))
vyarr=np.zeros(len(tarr))
axarr=np.zeros(len(tarr))
ayarr=np.zeros(len(tarr))
apxarr=np.zeros(len(tarr))
apyarr=np.zeros(len(tarr))
aZpxarr=np.zeros(len(tarr))
aZpyarr=np.zeros(len(tarr))
aFZp=np.zeros(len(tarr))
aF=np.zeros(len(tarr))
i=0
R=2.0
r=R
omega=1.0
for t in tarr:
xarr[i]=R*omega*t-r*sin(omega*t)
yarr[i]=R-r*cos(omega*t)
i+=1
vxarr=np.diff(xarr)
vyarr=np.diff(yarr)
axarr=np.diff(vxarr)
ayarr=np.diff(vyarr)
#Kruemmungsradius
#vsquared
for i in range(len(tarr)-2):
v2=vxarr[i]*vxarr[i]+vyarr[i]*vyarr[i]
av=vxarr[i]*axarr[i]+vyarr[i]*ayarr[i]
apxarr[i]=av*vxarr[i]/v2
apyarr[i]=av*vyarr[i]/v2
aZpxarr[i]=axarr[i]-apxarr[i]
aZpyarr[i]=ayarr[i]-apyarr[i]
aF[i]=sqrt(axarr[i]*axarr[i]+ayarr[i]*ayarr[i])
aFZp[i]=sqrt(aZpxarr[i]*aZpxarr[i]+aZpyarr[i]*aZpyarr[i])
plt.figure()
plt.subplot(211,aspect='equal',adjustable='box',title='Reference frame "Street": velocity and acceleration')
plt.plot(xarr,yarr,'k')
plt.hold(1)
plt.quiver(xarr[::20],yarr[::20],vxarr[::20],vyarr[::20],color='r',label='velocity')
plt.hold(1)
plt.quiver(xarr[::20],yarr[::20],axarr[::20],ayarr[::20],color='g',label='acceleration')
plt.ylim([0,max(yarr)])
plt.xlim([0,max(xarr)])
#plt.axes().set_aspect('equal')
#pl.show()
#plt.axes().set_aspect('equal')
plt.subplot(212,aspect='equal',adjustable='box',title='Reference frame "Street": Tangent and Centripetal Force')
#plt.figure()
plt.plot(xarr,yarr,'k')
plt.hold(1)
plt.quiver(xarr[::20],yarr[::20],apxarr[::20],apyarr[::20],color='b')
plt.quiver(xarr[::20],yarr[::20],aZpxarr[::20],aZpyarr[::20],color='y')
plt.ylim([0,max(yarr)])
plt.xlim([0,max(xarr)])
plt.savefig('centripetal_force_vs_external_force_vectors.svg')
#plt.axes().set_aspect('equal')
#plt.show()
plt.figure()
plt.title("External Force, tangent and centripetal components")
plt.plot(axarr,ayarr,'g', label='External Force')
plt.hold(1)
plt.plot(aZpxarr,aZpyarr,'y.', label='Centripetal Force')
plt.plot(apxarr,apyarr,'b.',label='Tangent Force')
plt.ylim([min(min(ayarr),min(aZpyarr),min(apyarr)),max(max(ayarr),max(aZpyarr),max(apyarr))*1.6])
plt.legend()
plt.axes().set_aspect('equal')
plt.savefig('centripetal_force_vs_external_force_circles.svg')
plt.figure()
plt.title('External Force and centripetal component vs. time')
plt.hold(1)
plt.plot(tarr,aFZp,'y',label='centripetal component')
plt.plot(tarr,aF,'g',label='External Force')
plt.legend(loc='lower left')
plt.xlim([0,tarr[len(tarr)-3]])
plt.savefig('centripetal_force_vs_external_force_time_series.svg')
#plt.show()
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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