Lesson 15
Lagrange's Equations with Undetermined Multipliers

Name:etp Section:M2 Start Time:12:53:2 Instructor:pate Course:355


1) Consider the system shown to the right. The orange disk rolls without slipping down the blue ramp. It would be possible to write the Lagrangian for this system either (a) using both y and q as generalized coordinates, or (b) using only y or q as the proper coordinate. Explain first of all why this is true (it really is). Then explain what would be different about the way you'd have to set up your equations in the two cases (a) and (b).




2) Consider the double Atwood machine shown in the figure and discussed in Example 7.8. The ropes on pulley 1 and pulley 2 have lengths l1 and l2 respectively. Suppose you want to determine the equations of motion for the masses in this system. It is possible to use Lagrange undetermined multipliers rather than setting it up as in Example 7.8. For the system as shown in this figure,

[Note: To make the typing easier, feel free to refer to the time derivative of x1 as "x1-dot", for example.]




3) Why are Lagrange undetermined multipliers useful?

  1. they represent the forces of constraint
  2. they permit use of a greater number of coordinates by providing the ability to include constraints
  3. both a and b above
  4. none of the above




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