Effect of inertia on laminar swimming and flying of an assembly of rigid spheres in an incompressible viscous fluid

摘要

A mechanical model of swimming and flying in an incompressible viscous fluidin the absence of gravity is studied on the basis of assumed equations ofmotion. The system is modeled as an assembly of rigid spheres subject toelastic direct interactions and to periodic actuating forces which sum to zero.Hydrodynamic interactions are taken into account in the virtual mass matrix andin the friction matrix of the assembly. An equation of motion is derived forthe velocity of the geometric center of the assembly. The mean power iscalculated as the mean rate of dissipation. The full range of viscosity iscovered, so that the theory can be applied to the flying of birds, as well asto the swimming of fish or bacteria. As an example a system of three equalspheres moving along a common axis is studied.