Skinner-Rusk approach to time-dependent mechanics

TL;DR

This paper extends the Skinner-Rusk geometric approach from autonomous to time-dependent classical mechanical systems, providing a unified framework for analyzing such systems.

Contribution

It introduces a novel extension of the Skinner-Rusk formalism to handle time-dependent mechanics, broadening its applicability.

Findings

Unified geometric framework for time-dependent systems

Extension of Skinner-Rusk formalism to non-autonomous cases

Potential for improved analysis of classical mechanics problems

Abstract

The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent framework.