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Derivation of the generalized forces of constraint using Lagrange multipliers in d'Alembert's principle
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Classroom Contents
Lagrange Multipliers and Constraint Forces - Nonholonomic Constraints - Downhill Race Various Shapes
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- 1 Derivation of the generalized forces of constraint using Lagrange multipliers in d'Alembert's principle
- 2 how generalized forces are connected with the Newtonian forces and moments of constraint for bodies.
- 3 The first example is 2 masses connected by a rigid rod, that is, a baton or dumbbell, with a 'wheel' underneath one of the masses, also called a knife-edge constraint or 'ice skate'. We solve for th…
- 4 We consider a pivoted-2 mass version with with wheel constraints called the roller racer (also known as a "Twistcar", "Plasma car", "Ezy Roller").
- 5 We consider another example, of a rigid body, a disk, rolling down a hill. The constraint here is rolling without slipping, and we solve for the Lagrange multiplier, as well as the force and moment …
- 6 We consider different round rigid bodies with different mass distributions and attempt to
- 7 predict which one will win a downhill race. It turns out the moment of inertia plays an important role.
