16.13: Sistemas de coordenadas
- Page ID
- 69948
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Coordenadas cartesianas
2 dimensiones: elemento de área:\(dA=dx.dy\).
3 dimensiones: elemento de volumen:\(dV=dx.dy.dz\).
Coordenadas polares
- \(x=r\cos\theta\)
- \(y=r\sin\theta\)
- \(r^2=x^2+y^2\)
- \(tan \theta=y/x\)
- \(dA=r.dr.d\theta\)
Coordenadas esféricas
- \(x=r\sin\theta\cos\phi\)
- \(y=r\sin\theta\sin\phi\)
- \(z=r\cos\theta\)
- \(r^2=x^2+y^2+z^2\)
- \(\theta=\cos^{-1}\left[\frac{z}{\sqrt{x^2+y^2+z^2}} \right]\)
- \(\phi=\tan^{-1}\left(\frac{y}{x}\right)\)
- \(dV=r^2\sin{\theta}dr.d\phi.d\theta\)