A continuum model for the orbit evolution of self-propelled ‘smart dust’ swarms

Abstract

A continuity equation is developed to model the evolution of a swarm of self-propelled ‘smart dust’ devices in heliocentric orbit driven by solar radiation pressure. These devices are assumed to be MEMs-scale (micro-electromechanical systems) with a large area-to-mass ratio. For large numbers of devices it will be assumed that a continuum approximation can be used to model their orbit evolution. The families of closed-form solutions to the resulting swarm continuity equation then represent the evolution of the number density of devices as a function of both position and time from a set of initial data. Forcing terms are also considered which model swarm sources and sinks (device deposition and device failure). The closed-form solutions presented for the swarm number density provide insights into the behaviour of swarms of self-propelled ‘smart dust’ devices an can form the basis of more complex mission design methodologies.