ECS221L5

# ECS221L5 - Forces in Space Force F is defined by magnitude F two angles and and point of application(origin y z F x Rectangular Components Given

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Forces in Space Force F is defined by magnitude F, two angles θ and φ , and point of application (origin). x y z F θ φ

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Rectangular Components Given the size F and angles θ , φ obtain components F x , F y , F z of force F . Step One. F =F h +F y F h = F sin θ F y = F cos θ x y z F θ φ
… more Step Two . F h = F x + F z , F = F x + F y + F z F x = F h cos φ , F z = F h sin φ F x = F cos φ sin θ F y = F cos θ F z = F sin φ sin θ x y z F h θ φ

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… more Given the components F x , F y , F z of force F , obtain magnitude F and angles θ , φ . x y z F h θ φ ( 29 2 y 2 h F F F + = ( 29 2 z 2 x h F F F + = ( 29 2 z 2 y 2 x F F F F + + = h x 1 y 1 F F cos F F cos θ - - = = φ
Direction Cosines Direction cosines θ x , θ y , θ z . F x = F cos θ x F y = F cos θ y F z = F cos θ z F x F y F z θ x θ y θ z

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The Unit Vector k F = F x i + F y j + F z k F x , F y , F z scalar components F x , F y , F z vector components F = F (cos θ x i + cos θ y j + cos θ z k ) F = F λ , λ is a unit vector in direction F

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## This note was uploaded on 04/02/2012 for the course ECS 221 taught by Professor Macnamara during the Fall '08 term at Syracuse.

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ECS221L5 - Forces in Space Force F is defined by magnitude F two angles and and point of application(origin y z F x Rectangular Components Given

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