{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 563 Mechanical Vibrations Lecture #6 Lagrange’s Method for Deriving Equations of Motion (examples)
Image of page 1

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

View Full Document Right Arrow Icon
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
Image of page 2
2 Eliminate constraints (keep x 2 and θ 1 ) Example Rolling Disc on a Moving Cart
Image of page 3

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

View Full Document Right Arrow Icon
3 Q θ 1 * = F i , nc ( ) i = 1 N r i θ 1 = f ( t ) i i = 1 N x 2 + D 2 θ 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 θ 1 i x 2 = f ( t ) i 1 i = f ( t ) Example Rolling Disc on a Moving Cart
Image of page 4
4 Example Rolling Disc on a Moving Cart
Image of page 5

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

View Full Document Right Arrow Icon
Torque Example Rolling Disc on Incline 5 Torque, τ (t) , acting about point C τ (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
Image of page 6
Explanation
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern