lecture710

# lecture710 - j = x − a sin − x a i + a cos − x a j...

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ME 563 Mechanical Vibrations Lecture #7 Calculating Generalized Forces in Lagrange’s Equations

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Example Rolling Disc on Incline 1 Force, p(t) , connected at point C Force, p(t) , connected at point B p(t) p(t)
Example Rolling Disc on Incline (Recall) 2 p(t) Calculate generalized forces (for degree of freedom, x ): r C = x i r C x = i

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Example Rolling Disc on Incline (New) 3 p(t) Calculate generalized forces (for degree of freedom, φ ): r C = a i r C ∂φ = a i
Example Rolling Disc on Incline (New) 4 p(t) Calculate generalized forces (for degree of freedom, x ): r B = x a sin φ ( ) i + a cos ( )

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Unformatted text preview: j = x − a sin − x a i + a cos − x a j ∂ r B ∂ x = 1 + cos − x a i + sin − x a j p attached to B Example Rolling Disc on Incline (New) 5 p(t) Calculate generalized forces (for degree of freedom, φ ): p attached to B Sprung Pendulum Example 6 r θ g f(t) Calculate generalized forces (for degree of freedom, r ): Sprung Pendulum Example 7 r θ g f(t) Calculate generalized forces (for degree of freedom, ):...
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lecture710 - j = x − a sin − x a i + a cos − x a j...

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