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Lagrange Multipliers E,=0 A disc of mass m and radius R has a string wrapped around it with the end attached to a fixed support. The string is unwinding as the disk falls. Take I = mR². We will denote by r the length of the string and by 0', the angular speed of the disc. %3D R 1. Express the constraint equation, of the rolling without slipping disc, in polar coordinate (r,0) 2. Write the modified Lagrangian equation 3. Derive the differential equations of motion for each coordinate 4. Calculate the Lagrange multiplier A, in terms of m, g 5. Calculate the equation of constraints Q, and Qo

Lagrange Multipliers E,=0 A disc of mass m and radius R has a string wrapped around it with the end attached to a fixed support. The string is unwinding as the disk falls. Take I = mR². We will denote by r the length of the string and by 0', the angular speed of the disc. %3D R 1. Express the constraint equation, of the rolling without slipping disc, in polar coordinate (r,0) 2. Write the modified Lagrangian equation 3. Derive the differential equations of motion for each coordinate 4. Calculate the Lagrange multiplier A, in terms of m, g 5. Calculate the equation of constraints Q, and Qo

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Lagrange Multipliers E,=0 A disc of mass m and radius R has a string wrapped around it with the end attached to a fixed support. The string is unwinding as the disk falls. Take I = mR2. We will denote by r the length of the string and by 0', the angular speed of the disc. R 1. Express the constraint equation, of the rolling without slipping disc, in polar coordinate (r,0) 2. Write the modified Lagrangian equation 3. Derive the differential equations of motion for each coordinate 4. Calculate the Lagrange multiplier A, in terms of m, g 5. Calculate the equation of constraints Q, and Qo
Transcribed Image Text:Lagrange Multipliers E,=0 A disc of mass m and radius R has a string wrapped around it with the end attached to a fixed support. The string is unwinding as the disk falls. Take I = mR2. We will denote by r the length of the string and by 0', the angular speed of the disc. R 1. Express the constraint equation, of the rolling without slipping disc, in polar coordinate (r,0) 2. Write the modified Lagrangian equation 3. Derive the differential equations of motion for each coordinate 4. Calculate the Lagrange multiplier A, in terms of m, g 5. Calculate the equation of constraints Q, and Qo
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