The connection between the calculus of variations and mechanics is essentially as old as calculus. In many problems in mechanics, there is a correspondence between the physical force/moment balance equations of Newton/Euler and the Euler-Lagrange equations of the calculus of variations for a certain physically meaningful Lagrangian. This correspondence curiously breaks down in the presence of nonholonomic constraints, e.g., rolling constraints. There is a constrained calculus of variations problem in the presence of such constraints, but the Euler-Lagrange equations for this problem generally do not agree with the physical equations of motion. I will chat about this and try to describe some recent work on the connections between the physical equations of motion and the constrained Euler-Lagrange equations.

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