lecture610 - ME 563 Mechanical Vibrations Lecture #6...

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ME 563 Mechanical Vibrations Lecture #6 Lagrange’s Method for Deriving Equations of Motion (examples)
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Example Rolling Disc on a Moving Cart 1 K1 f(t) No slip 3D/4 D K2 M1,Icm M2 g x 2 θ 1 A B
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2 Eliminate constraints (keep x 2 and θ 1 ) Example Rolling Disc on a Moving Cart
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3 Q θ 1 * = F i , nc ( ) i = 1 N r i ∂θ 1 = f ( t ) i i = 1 N x 2 + D 2 1 i ∂θ 1 = f ( t ) i D 2 i = D 2 f ( t ) Q x 2 * = F i , nc ( ) i = 1 N r i x 2 = f ( t ) i i = 1 N x 2 + D 2 1 i x 2 = f ( t ) i 1 i = f ( t ) Example Rolling Disc on a Moving Cart
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4 Example Rolling Disc on a Moving Cart
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Torque Example Rolling Disc on Incline 5 Torque, τ (t) , acting about point C (t) In the last slide, we considered forces but what about a torque applied at the center of mass of the rolling disc? How do we compute the generalized “force.” We need to think in terms of torque acting about a point
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lecture610 - ME 563 Mechanical Vibrations Lecture #6...

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