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# lec07 - Kinematics of Rigid Bo dies 1 2.003J/1.053J...

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Kinematics of Rigid Bodies 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/28/2007 Lecture 7 2-D Motion of Rigid Bodies - Kinematics Kinematics of Rigid Bodies Williams 3-3 (No method of instant centers) ”Kinematics” - Description and analysis of the motions of objects without con- sideration of the forces and torques causing them. Angular Velocity Deﬁne Angular Velocity Figure 1: Rigid body in inertial frame. Figure by MIT OCW. The angular velocity of the rigid body: ω = e ˆ z dt ω is a property of the body. ω is independent of the choice of ’painted line’ or the reference ﬁxed direction (Bedford Fowler 6-2, 6-3)

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 Kinematics of Rigid Bodies Calculation of Velocity of a Point P on a Rotating Rigid Body Figure 2: Rotating Rigid Body. O is ﬁxed in the frame. Rotation axis passes through O . Figure by MIT OCW. For any point on the body P: v = ω × r p More generally, for any vector R on the body: R = r 2 r 1 Figure 3: Rigid Body Rotating. Figure by MIT OCW. Therefore:
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3

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lec07 - Kinematics of Rigid Bo dies 1 2.003J/1.053J...

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