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CS545_Lecture_10

CS545_Lecture_10 - CS545-Contents X Lagrange's Method of...

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CS545—Contents X Lagrange’s Method of Deriving Equations of Motion for Rigid Body Systems Lagrange’s Equation Generalized Coordinates Potential Energy Kinetic Energy Properties of the Dynamics Equations Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545
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Lagrange’s Equations The Lagrangian (a potential function) is Lagrange’s Equations are: Generalized Coordinates Any set of coordinates that complete describes a dynamical system Lagrangian is coordinate free Generalized Forces The corresponding forces or torques applied along the generalized coordinates Includes friction, external, and motor forces (non conservative forces) L = T - U d dt L ˙ θ i L θ i = τ i
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Example: Pendulum Kinetic Energy Potential Energy Lagrangian Equation of Motion m l Motor Gravity g I ˙ ˙ θ + mgl sin θ ( ) = τ T = 1 2 I ˙ θ 2 U = mgl 1 cos θ ( ) L = T - U θ τ
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Kinetic Energy In General: Problems
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