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Tanya Schmah and Cristina Stoica
Nonholonomic Hamilton-Jacobi equation and integrability
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion.
We give an intrinsic proof of a nonholonomic analogue of the Hamilton-Jacobi theorem.
Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems.
The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints.
The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton-Jacobi theory does.
In particular, we build on the work by Iglesias-Ponte, de Léon, and Martín de Diego  so that the conventional method of separation of variables applies to some nonholonomic mechanical systems.
We also show a way to apply our result to systems to which separation of variables does not apply.