# lec09 - Cite as Thomas Peacock and Nicolas...

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Unformatted text preview: 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 Kinetics of Rigid Bodies 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 3/7/2007 Lecture 9 2D Motion of Rigid Bodies: Kinetics, Poolball Example Kinetics of Rigid Bodies Angular Momentum Principle for a Rigid Body Figure 1: Rigid Body rotating with angular velocity ω . Figure by MIT OCW. H B = r i × m i ( v c + ω × ρ i ) i After some steps (see Lecture 8): H B = r × P + m i ρ × ω × ρ c i i i We now use: a × b × c = ( a · c ) b − ( a · b ) c ρ × ω × ρ = ρ i 2 ω − ( ω · ρ ) ρ i i i i = ρ 2 i ω 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 Kinetics of Rigid Bodies For 2-D motion, ω · ρ = because the vectors are ⊥ . For 3-D, this term does i not have to be 0. H B = r c × P + m i ρ 2 ω i i = r c × P + I c ω I c : Moment of Inertia. I c = i m i ρ i 2 (Intrinsic Property of Rigid Body) Example:...
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lec09 - Cite as Thomas Peacock and Nicolas...

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