Classical counterparts of shortcuts to adiabaticity in nonlinear dissipative Lagrangian systems

TL;DR

This paper extends the concept of shortcuts to adiabaticity from quantum systems to classical nonlinear dissipative Lagrangian systems, demonstrating inverse engineering, error analysis, and correction methods.

Contribution

It introduces a classical framework for implementing shortcuts to adiabaticity, including inverse engineering, error quantification, and a single-shot correction technique.

Findings

Inverse engineering yields force and torque profiles for classical systems.

Geometric coupling amplifies errors and residual energy.

Mid-course measurement correction reduces deviations while maintaining smooth inputs.

Abstract

Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$\theta$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.