ME 242 Lecture 8 02.06 - ME 242 Dynamics February 6 2009 Today's Key Concepts Review of Chapter 2 Cartesian Coordinates Coordinate Transformation Array

# 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 vP=ddtXYZrP/O=˙ x i+˙ y j+˙ z kaP=ddtXYZvP=˙ ˙ x i+˙ ˙ y j+˙ ˙ z krP/O=xi+y j+zkθb1 b2 cos θ00001cos θ-sin θsin θb2 jib1 b3 kθθθjicos θcos θb1=cosθi+sinθjb2=sinθi+cosθj3 Special cases vdv=adxv22=v12+2a(x2x1)v22=v12+2a(x)dxx1x2x2=x1+va(v)dvv1v2
2 Polar (2D) & Cylindrical (3D) • Position • Velocity • Acceleration aP=˙ r r˙ θ2)er+(2˙ r ˙ θ+r˙ ˙ θ)eθ+˙ ˙ z krP/O=rer+zkvp=˙ r er+r˙ θeθ+˙ z kPath Coordinates vp=vetaP=˙ v et+v2rcenRelative Motion rA/O=rB/O+rA/BvA=vB+vA/BaA=aB+aA/BDegrees of Freedom DOF = number of independent directions of motion possible 1-DOF Constraints •x1and x2