FormulaFL

FormulaFL - Vector Formulae Vector functions A (r ), B (r...

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Vector Formulae Vector functions ~ A ( ~ r ), ~ B ( ~ r ), ~ C ( ~ r ). Scalar functions f ( ~ r ), g ( ~ r ). ~ A · ( ~ B × ~ C ) = ~ B · ( ~ C × ~ A ) = ~ C · ( ~ A × ~ B ) (1) ~ A × ( ~ B × ~ C ) = ~ B ( ~ A · ~ C ) - ~ C ( ~ A · ~ B ) (2) ~ ( fg ) = f ( ~ g ) + g ( ~ f ) (3) ~ ( ~ A · ~ B ) = ~ A × ( ~ ∇ × ~ B ) + ~ B × ( ~ ∇ × ~ A ) + ( ~ A · ~ ) ~ B + ( ~ B · ~ ) ~ A (4) ~ ∇ · ( f ~ A ) = f ~ ∇ · ~ A + ~ f · ~ A (5) ~ ∇ × ( f ~ A ) = f ~ ∇ × ~ A + ~ f × ~ A (6) ~ ∇ · ( ~ A × ~ B ) = ~ B · ( ~ ∇ × ~ A ) - ~ A · ( ~ ∇ × ~ B ) (7) ~ ∇ × ( ~ A × ~ B ) = ( ~ B · ~ ) ~ A - ( ~ A · ~ ) ~ B + ~ A ( ~ ∇ · ~ B ) - ~ B ( ~ ∇ · ~ A ) (8) ~ ∇ × ( ~ ∇ × ~ A ) = ~ ( ~ ∇ · ~ A ) - ∇ 2 ~ A (9) Orthogonal Curvillinear Coordinates ~ r = ( x ( u, v, w ) , y ( u, v, w ) , z ( u, v, w )) Orthorgonality: ˆ e 1 = ∂~ r ∂u ± ± ± ± ∂~ r ∂u ± ± ± ± ± , ˆ e 2 = ∂~ r ∂v ± ± ± ± ∂~ r ∂v ± ± ± ± ± , ˆ e 3 = ∂~ r ∂w
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FormulaFL - Vector Formulae Vector functions A (r ), B (r...

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