Chiral knife edge: A simplified rattleback to illustrate spin inversion.

We present the chiral knife edge rattleback, an alternative version of previously presented systems that exhibit spin inversion. We offer a full treatment of the model using qualitative arguments, analytical solutions as well as numerical results. We treat a reduced, one-mode problem which not only contains the essence of the physics of spin inversion, but that also exhibits an unexpected connection to the Chaplygin sleigh, providing insight into the nonholonomic structure of the problem.

Optical mechanical analogy and nonlinear nonholonomic constraints.

In this paper we establish a connection between particle trajectories subject to a nonholonomic constraint and light ray trajectories in a variable index of refraction. In particular, we extend the analysis of systems with linear nonholonomic constraints to the dynamics of particles in a potential subject to nonlinear velocity constraints. We contrast the long time behavior of particles subject to a constant kinetic energy constraint (a thermostat) to particles with the constraint of parallel velocities.

Optical mechanical analogy and Hamiltonization of a nonholonomic system.

It is well known that there is an analogy between optics and mechanics that prompted much of the classical theory of mechanics and indeed extended it to the theory of quantum mechanics. We develop here an optical mechanical analogy for a prototypical nonholonomic mechanical system, a knife edge moving on a plane under the influence of a potential. We show that this approach is related to but different from the classical theory of Hamiltonization of nonholonomic systems.

Nonholonomic double-bracket equations and the Gauss thermostat.

In this Rapid Communication we consider certain equations that arise from imposing a constant kinetic-energy constraint on a one-dimensional set of oscillators. This is a nonlinear nonholonomic constraint on these oscillators and the dynamics are consistent with Gauss's law of least constraint. Dynamics of this sort are of interest in nonequilibrium molecular dynamics.

Quantization of a nonholonomic system.

In this Letter, we consider the problem of quantizing a nonholonomic system. This is highly nontrivial since such a system, which is subject to nonholonomic constraints, is not variational (or Hamiltonian). Our approach is to couple the system to a field which enforces the constraint in a suitable limit.