Silindirik ve küresel koordinatlarda del

Bu liste eğrisel koordinat sistemleri ile çalışılırken genel olarak kullanılan vektör hesabı formüllerinin bir listesidir.

Not

  • Bu sayfada standart fizik gösterim kullanır. küresel koordinatlar için, θ açısı yarıçap vektörünün z ekseni ile olan açısıdır ve Söz konusu noktaya orijinden bağlanır. ϕ açısı yarıçap vektörünün x-y yüzeyine izdüşümü ile ve x ekseni ile olan açıdır. Bazı kaynaklar θ ve ϕ yi ters tanıtırlar, bu anlam bağlamında böyle bir bağlantı kurulmamalıdır.
  • atan2(y, x) fonsiyonu kendi etki ve görüntü nedeniyle matematiksel fonksiyon arctan(y/x) yerine kullanılabilir, klasik arctan(y/x) görüntüsü (-π/2, +π/2)aralığında idi, buradaki atan2(y, x) (-π, π] aralığındadır. (Küresel koordinatlarda Del için ifadelerin düzeltilmesi gerekebilir)
  • Dönüşümler kartezyen koordinatlardan silindirik ve küreseledir.
del operatörü ile Silindirik küresel ve parabolik silindirik koordinatlar tablosu
işlem Kartezyen koordinatlar (x, y,z) Silindirik koordinatlar (ρ,φ,z) Küresel koordinatlar (r,θ,φ) Parabolik silindrik koordinatlar (σ,τ,z)
Koordinat Tanımları
Birim Vektölerin Tanımları
Bir vektör alanı
Gradyan

Diverjans

Curl
Laplace işlemcisi
Vektör Laplasyeni
Malzeme türevi[1]

Diferansiyel yer değiştirme
Diferansiyel yüzey normali
Diferansiyel hacim
önemli birtakım hesaplama kuralları:
  1. (Laplasyen)
  2. (Vektör çarpımı için Lagrange formülünü kullanarak)

Ayrıca bakınız

Kaynakça

  1. ^ Weisstein, Eric W. "Convective Operator". Mathworld. 3 Mart 2016 tarihinde kaynağından arşivlendi. Erişim tarihi: 23 Mart 2011. 

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