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ME 242 Lecture 8 02.06

ME 242 Lecture 8 02.06 - ME 242 Dynamics February 6 2009...

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1 ME 242 Dynamics February 6, 2009 Eric Wang Today’s Key Concepts Review of Chapter 2 Cartesian Coordinates Coordinate Transformation Array Polar Coordinates Path Coordinates Relative Motion Degrees of Freedom • Constraints Importance of Reference Frames Cartesian Coordinates • Position • Velocity • Acceleration v P = d dt XYZ r P / O = ˙ x i + ˙ y j + ˙ z k a P = d dt XYZ v P = ˙ ˙ x i + ˙ ˙ y j + ˙ ˙ z k r P / O = xi + y j + zk θ b 1 b 2 cos θ 0 0 0 0 1 cos θ -sin θ sin θ b 2 j i b 1 b 3 k θ θ θ j i cos θ cos θ b 1 = cos θ i + sin θ j b 2 = sin θ i + cos θ j 3 Special cases vdv = adx v 2 2 = v 1 2 + 2 a ( x 2 x 1 ) v 2 2 = v 1 2 + 2 a ( x ) dx x 1 x 2 x 2 = x 1 + v a ( v ) dv v 1 v 2
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2 Polar (2D) & Cylindrical (3D) • Position • Velocity • Acceleration a P = ˙ r r ˙ θ 2 ) e r + (2˙ r ˙ θ + r ˙ ˙ θ ) e θ + ˙ ˙ z k r P / O = re r + zk v p = ˙ r e r + r ˙ θ e θ + ˙ z k Path Coordinates v p = ve t a P = ˙ v e t + v 2 r c e n Relative Motion r A / O = r B / O + r A / B v A = v B + v A / B a A = a B + a A / B
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