formulas - PHY 3221: Mechanics I Fall Term 2010 Formula...

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Unformatted text preview: PHY 3221: Mechanics I Fall Term 2010 Formula sheet A · ( B × C ) = B · ( C × A ) = C · ( A × B ) ≡ ABC A × ( B × C ) = ( A · C ) B − ( A · B ) C ( A × B ) · ( C × D ) = A · [ B × ( C × D )] = A · [( B · D ) C − ( B · C ) D ] = ( A · C )( B · D ) − ( A · D )( B · C ) ( A × B ) × ( C × D ) = [( A × B ) · D ] C − [( A × B ) · C ] D = ( ABD ) C − ( ABC ) D = ( ACD ) B − ( BCD ) A v = ˙ r e r + r ˙ θ e θ + r sin θ ˙ φ e φ a = parenleftBig ¨ r − r ˙ θ 2 − r ˙ φ 2 sin 2 θ parenrightBig e r + parenleftBig 2˙ r ˙ θ + r ¨ θ − r ˙ φ 2 sin θ cos θ parenrightBig e θ + parenleftBig 2˙ r ˙ φ sin θ + 2 r ˙ θ ˙ φ cos θ + r ¨ θ sin θ parenrightBig e φ v = ˙ r e r + r ˙ φ e φ + ˙ z e z a = parenleftBig ¨ r − r ˙ φ 2 parenrightBig e r + parenleftBig r ¨ φ + 2˙ r ˙ φ parenrightBig e φ + ¨ z e z summationdisplay k ε ijk ε lmk = δ il δ jm − δ im δ jl summationdisplay j,k ε ijk ε ljk = 2 δ il summationdisplay...
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This note was uploaded on 12/15/2011 for the course PHY 3221 taught by Professor Chan during the Spring '08 term at University of Florida.

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formulas - PHY 3221: Mechanics I Fall Term 2010 Formula...

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