2D Equations of Motion

2D Equations of Motion - Rigid-Body Planar Equations of...

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Unformatted text preview: Rigid-Body Planar Equations of Motion Consider a rigid body as a system of particles: 1) Translational Equations of Motion: From section 13.3: G a m F = These are the translational equations of motion that state the sum of all the external forces acting on the body equals the acceleration of the bodys center-of-mass G. Scalar equations: Gy y Gx x ma F ma F = = 2) Rotational Equations of Motion: Consider the i th particle: where forces external all of resultant F ns) interactio (particle forces internal all of resultant f i i = = Summing the moments of force about point P: i i i i pi a m r f r F r M = + = 0 (when summed over all particles) = 2 Note: r r x a a 2 p i + = (relative motion analysis equation) Now , )) r r ( ) r x r a r ( m ) r r x a ( m r M 2 p i 2 p i pi + = + = ( k , j a i a a , j y i x r Let py px p = + = + = k ) r m xa m ya (-m )) j y i (x k j y i x j a i (a ) j y i ((x m M 2 i py i px i py px i...
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This note was uploaded on 04/05/2012 for the course ME 324 taught by Professor Neptune during the Spring '08 term at University of Texas at Austin.

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2D Equations of Motion - Rigid-Body Planar Equations of...

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