Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 38C / c / Solution

At negligible Reynolds number, the Stokes equations and their no-slip boundary conditions are linear in velocity. Scaling or superposing a prescribed rigid translation therefore scales or superposes the resulting stress and total hydrodynamic force. Hence, for a fixed rod orientation,The minus sign records that viscous drag opposes motion, and $\mathbf{R}$ is the translational hydrodynamic resistance matrix.

Solved by gpt-5.6-sol high.