기록

33. Angular Velocity Instantaneous Axis of Rotation Angular Velocity: $ \omega =\frac{d\Theta }{dt}=\dot{\Theta } $ Velocity: $ v=R\frac{d\Theta }{dt}=R\omega $ $ \dot{\vec{r}}=\vec{v} $ $ R=r\sin \alpha $ $ v=R\omega =r\omega \sin \alpha $ $ \Rightarrow \vec{v}=\vec{\omega }\times \vec{r} $ 34. Infinitesimal Rotation Infinitesimal Rotation can be represented by vector. Finite Rotation cannot be..

13. Rotating Coordinate Axes 1) Counterclockwise about the $ x_{3} $-axis $ x_{1}'=x_{2}, x_{2}'=-x_{1}, x_{3}'=x_{3} $ $ \lambda _{11}=\lambda _{13}=\lambda _{22}=\lambda _{23}=\lambda _{31}=\lambda _{32}=0 $ $ \lambda _{12}=\cos (x_{1}',x_{2})=1 $ $ \lambda _{21}=\cos (x_{2}',x_{1})=-1 $ $ \lambda _{33}=\cos (x_{3}',x_{3})=1 $ $ \Rightarrow \vec{\lambda_{1}} =\bigl(\begin{smallmatrix} 0 & 1 & ..

6. Properties of Rotation Matrices $ (\alpha ,\beta ,\gamma )\rightarrow (\alpha ',\beta ',\gamma ') $ $ (x_{1},x_{2},x_{3}) $ coordinate에서 $ \Theta $ 만큼 회전한 $ (x_{1}',x_{2}',x_{3}') $ coordinate 1) $ \cos ^{2}\alpha +\cos ^{2}\beta +\cos ^{2}\gamma =1 $ $ x_{1}=r\cos \alpha , x_{2}=r\cos \beta , x_{3}=r\cos \gamma $ $ r^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=r^{2}\cos ^{2}\alpha +r^{2}\cos ^{2}\beta..