lecture7 notes

# Drdd depending on coordinate system dvol a ha dxa

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sin θ ) ∂ er · ∂ r er + 1 eθ ∂r eθ + eφ · cos θeφ r s1 θ � ∂� � � � in r� cos θ r sin θ 2 �� � · eφ = (er · � ∂ � ∂ r )eφ er · ∂ r er � ∂� = �v �·� = ∂ vr ∂r ∂ � � ∂� ∂ θ )eθ + (eφ · ∂ φ )eφ 1 �∂� r + eφ ( ∂ φ · eφ ) = + (eθ · � + eθ · � + 2 vr + 1 ( ∂vθθ + r r∂ cos θ sin θ vθ ) + 1 r sin θ · 0 ∂ vφ ∂φ ∂ product rule w/ ∂ r product rule w/ ∂∂θ product rule w/ ∂∂φ Σa (ha dxa )ea � ea · eb = δab �� ⎧ ⎪dxdydz ⎪ ⎪ ⎪ ⎪ ⎪2 ⎨r sin θdrdθdφ (depending on coordinate system) d(vol) = Πa (ha dxa ) = ⎪.... ⎪ ⎪ ⎪ ⎪ ⎪ ⎩.... d� = x Jacobian... okay...?? ⎧ ⎪da�e = h dx · h · dx ⎪ || �a b b i i ⎪ ⎨ da = r2 dΩer � ⎪r ⎪ ⎪ ⎩dΩ = sin θdθdφ d(vol) = dxdydz = dvdudw ||J || eb × ei �� where ||J || is the Jacobian. Spherical C...
View Full Document

## This note was uploaded on 01/23/2014 for the course PHYS 8.022 taught by Professor Shaw during the Fall '06 term at MIT.

Ask a homework question - tutors are online