ME 242 Lecture 33 04.27

ME 242 Lecture 33 04.27 - 1 ME 242 Dynamics April 27, 2009...

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Unformatted text preview: 1 ME 242 Dynamics April 27, 2009 Eric Wang Todays Key Concepts Chapter 8: 3D motion of Rigid Bodies We will only do kinematics in 3D Spherical coordinates Angular velocity in 3D Angular acceleration in 3D Polar Coordinates a m = ( r r 2 ) e r + (2 r + r ) e r m / O = re r v m = r e r + r e Polar Coordinates in 3D X Y Z Video Clip The Force is Strong X Y Z 2 Spherical Coordinates R m / O = Re R Introduce x-Z Plane R m / O = Re R = re r + R cos k 2 sets of polar coordinates r = R sin Coordinate Transformation Arrays cos 1 cos -sin sin e j i e r k k cos sin -sin cos 1 e e e r e e R k R m / O = Re R = R (sin e r + cos k ) = re r + R cos k Velocity & Acceleration a m = ( R R 2 R 2 sin 2 ) e R R m / O = Re R v m = R e R + R e + R sin e + 2 R + R R 2 sin(2 ) 2 e + 2 R...
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ME 242 Lecture 33 04.27 - 1 ME 242 Dynamics April 27, 2009...

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