{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

l_notes06

# l_notes06 - Lecture VI Calculus of Vector Functions dR dt 2...

This preview shows pages 1–2. Sign up to view the full content.

Lecture VI Calculus of Vector Functions R d 2 R Recall that d denotes the first-order derivative of R ( t ), and that dt 2 de- dt notes the second-order derivative of R ( t ). We introduce new notations for these R ˙ R ¨ R ( t ) = a 1 ( t ) ˆ i + a 2 ( t ) ˆ + a 3 ( t ) ˆ functions: d = R ( t ) and d 2 = R ( t ). Let j k . dt dt 2 Then the following differentiation rules stand: ˙ j + ˙ a 3 ( t ) ˆ 1. R ( t ) = a ˙ 1 ( t ) ˆ i + ˙ a 2 ( t ) ˆ k . ¨ a 1 ( t ) ˆ i + ¨ j a 3 ( t ) ˆ 2. R ( t ) = ¨ a 2 ( t ) ˆ + ¨ k . A ( t ) and Let B ( t ) be differentiable vector functions, and let a ( t ) be a differentiable scalar function. The following differentiation rules stand: dt ( ˙ ˙ 3. d A ( t ) + B ( t )) = A + B . 4. d A ( t )) = a ˙( t ) ˙ A ( t ) + a ( t ) A ( t ). dt ( a ( t ) dt ( ˙ A · B . 5. d A ( t ) · B ( t )) = A · B + ˙ 6. d A ( t ) × ˙ B + B ( t )) = A × A × B . dt ( ˙ R ( t ) be a unit vector function, Theorem 1 (Unit-Vector Theorem) Let R ( t ) = ˆ u ( t ) for all t . Then: u is perpendicular to that of ˆ 1. The direction of ˆ

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}