Moving regions in Euclidean space and Reynolds’ transport theorem

Abstract

This paper gives new demonstrations of Reynolds’ transport theorems for moving regions in Euclidean space. For moving volume regions the proof is based on differential forms and Stokes’ formula. Moving curves and surface regions are defined and the intrinsic normal time derivative is introduced. The corresponding surface transport theorem is derived using the partition of unity and the surface divergence theorem. A proof of the surface divergence theorem is also given.