ASE 365 - Lecture 22

ASE 365 - Lecture 22 - Analytical dynamics In contrast to...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Analytical dynamics In contrast to Newtonian ( F =m a ): – Work/energy based – Scalar, rather than vector – Bypasses constraint forces unless needed – System rather than individual components – Streamlines analysis—one EOM per DOF – Independent of coordinates chosen – More abstract, less “physical” Generalized coordinates Planar dumbbell example: m 1 m 2 L x y motion). (planar freedom of degrees 3 only but : s coordinate 4 j i r j i r 2 2 2 1 1 1 , y x y x + = + = satisfied. lly automatica is : Constraint : s" coordinate d generalize " as , in , choose Or, 2 2 1 2 2 1 2 2 1 1 2 2 1 2 1 ) ( ) ( ) sin (cos , ) sin (cos L y y x x m m L m m m L m y x y x c c c c c c c =- +- + + + = + +- = + = j i r r j i r r j i r θ θ θ θ θ r c θ r 1 r 2 (x2,y2 ) (x1,y1 ) assumed. is motion D- 3 and s constraint kinematic of number the is particles, of number the is where : freedom of degrees of Number c N c N n- = 3 ) , , ( ), , , ( ), , , ( ), , , ( ), , , ( ), , , ( , ) , , ( ), , , ( ), , , ( 2 1 2 1 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 1 1 1 2 1 1 1 n N N n N N n N N n n n n n n q q q z z q q q y y q q q x x q q q z z q q q y y q q q x x q q q z z q q q y y q q q x x = = = = = = = = = : tion) transforma e (coordinat s coordinate d generalize of terms in s coordinate physical Express Principle of virtual work variations to related ) ( antaneous neous/inst contempora arbitrary s) constraint kinematic with t (consisten admissible imagined zero) terms order- higher (so mal infinitesi : ... , , , nts displaceme virtual define First, • = • • • • → • 1 1 1 t z z y x N δ δ δ δ δ s. derivative als, differenti like handled be Can force. (reaction) constraint force, applied where : particle th on force Resultant = = = + = i i i i i N i i f F f F R , , 2 , 1 , N i W i i i i i i , , 2 , 1 , = = ⋅ ≡ = r R r R...
View Full Document

This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas.

Page1 / 19

ASE 365 - Lecture 22 - Analytical dynamics In contrast to...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online