Problem 3 A hoop of mass m and radius R, rolls without slipping down an inclined plane of angle a. The inclined plane of mass M moves horizontally. Let X be the abscissa of point O' with respect to 0, and s be the abscissa of the center of mass of the rolling hoop with respect to O'. Given: the moment of inertia of the hoop is I mR, and the condition of rolling without slipping is expressed ass = RO: 1. Write the Lagrangian of the system. 2. Assuming that the Lagrangian of the sy stem (inclined plane and hoop) is given by: L = ms" +(m + M)X" + ms'X'cos(a) + mg(s)sin(a) 3. Write the expression of the Lagrangian function

Problem 3 A hoop of mass m and radius R, rolls without slipping down an inclined plane of angle a. The inclined plane of mass M moves horizontally. Let X be the abscissa of point O' with respect to 0, and s be the abscissa of the center of mass of the rolling hoop with respect to O'. Given: the moment of inertia of the hoop is I mR, and the condition of rolling without slipping is expressed ass = RO: 1. Write the Lagrangian of the system. 2. Assuming that the Lagrangian of the sy stem (inclined plane and hoop) is given by: L = ms" +(m + M)X" + ms'X'cos(a) + mg(s)sin(a) 3. Write the expression of the Lagrangian function

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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