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# l4anno - Rectilinear Motion x(t F O rOP(t = x(t i v P(t =...

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Rectilinear Motion F O P x ( t) ( ) ( ) ( ) ( ) ( ) ( ) OP P P t x t t x t t x t = = = a r i v i i & && P moves along a straight path Suppress dependence on F

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Define Constraint Equations Pulley problems: Rope length is constant Relations between and Relations between and e.g. ( ) OA x r ( ) OB y r OA r OB r | | | | AB OB OA = r r r
Differentiate constraint equations w.r.t. time Constraint equations may be nonlinear in position components Derivative equations are linear in velocity and acceleration components

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Rectangular Cartesian Coordinates ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) OP P P t x t y t z t t x t y t z t t x t y t z t = + + = + + = + + r i j k v i j k a i j k & & & && && && Suppress dependence on F
Recipe ( ) 2 ( ) ( ) ( ) ( ) ( ( )) ( ) ( ) ( ( )) ( ) ( ) ( ) ( ( ' '' )) ( ) ( ( ( )) ( ) ) ( ) ' OP P OP P OP t t t x t y t x t x t t x t x t x t t x t x t x t x t x t y y y y = + = + = = + = = + + r i j i j v r i j a r i j & & & && && & && Given ( ), ( ) or ( ) Find remaining functions ( ), ( ) or ( ( ( )), ( ( )) an ' '' d ( ( )) Express ( ), ) Find ( ) and ( ) OP P P x t x t x x t x t x t x t x t x t y y t y t t t r v a & && & && Different colors denote difference functions (of t and x ) O OP r P ( ) y y x = x y

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