Abstract
Reciprocating motion of an active deformable particle in a homogeneous medium is studied theoretically. For generality, we employ a simple model derived from symmetry considerations for the center-of-mass velocity and elliptical and triangular deformations in two dimensions. We carry out, for the first time, a systematic investigation of the reciprocating motion of a self-propelled particle. It is clarified that spontaneous breaking of the front-rear asymmetry is essential for the reciprocating motion. Moreover, two routes are found for the formation of the reciprocating motion. One is a bifurcation from a motionless stationary state. The other is destabilisation of an oscillatory rectilinear motion.
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