R t r cos r sin the velocity in a plane v t

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Unformatted text preview: ith polar coordinates.  ©§ ¨¦ ©§ ¨¦ R t, r Cos , r Sin The velocity in a plane. ©§ ¨¦ ©§ ¨¦ V t, r Cos r Sin , r Sin ,0 Acceleration in a plane. § ¨¦ ©§ ©§ ¨¦ § ¨¦ ©§ A r Sin . r Cos r Sin ,0 The second term is the acceleration in the radial direction, the third is acceleration in the theta direction for a central force in polar coordinates. 0  0, r, ) ¢ £¢ L2 m2 r3 . 2Lr ,0 m r2 1 ©§ ¨¦ ©§ ¨¦ ©§ £¨¦ )) () ©§ ¨¦ A Cos , 0, 0, Sin t, r Cos , r Sin ,0  ¤ d ,0 dt 2 ! Not a pretty sight. For a central force, get rid of the theta dependence. ¡ ¢ ¤ ¥ L/ 2, and # $ " "   . ©§ ¨¦  § ¨¦ ©§ r Sin 2 ¢ £¢ . r Sin  § ¨¦ ©§ r Cos r Cos ©§ ¢ ¨¦ ©§ ¢ § ¨¦ ©§ ¢ § ¨¦ . 0, 2 r Sin . . 2r Cos 2 ¢ £¢ . , r Cos ,0 0. Make these substitution and rotate the quaternion to  § ¨¦ ©§ ¢ £¢ § ¨¦ ©§ ¢ £¢ ©§ ¢ ¨¦ ¤ d ,0 dt . 1, r Cos .. , r Sin  § ¨¦ ©§ ©§ ¨¦ .. , r Sin r Cos  § ¨¦ ©§...
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This note was uploaded on 09/30/2010 for the course MAE 123 taught by Professor 123 during the Spring '10 term at École Normale Supérieure.

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