Ultra-chaos of square thin plate in low Earth orbit

Due to its small mass and eccentricity, the motion of a piece of debris in low Earth orbit (LEO) may be chaotic. This paper demonstrates that ultra-chaos widely exists in the case of a square thin plate in LEO with a center of mass (COM) that is initially displaced from the axis of symmetry. Chaotic systems are well-known for their sensitive dependence on initial conditions, though their statistical properties are usually insensitive to small disturbances. However, a recent concept called ultra-chaos has been introduced to describe chaotic systems whose statistics are sensitive to even tiny disturbances. This paper demonstrates that ultra-chaos is widely exists in a square thin plate in LEO with a displaced COM from the axis of symmetry. The results show that an ultra-chaotic plate trajectory exhibits higher disorder than that of a normal plate, with a position deviation that can be two orders of magnitude larger than that of a normal-chaotic subsystem. Distinct from earlier findings concerning ultra-chaotic systems, the present study uncovers the manifestation of ultra-chaos in a physically constrained system devoid of periodic boundaries. Prior investigations of ultra-chaotic systems have featured at least one periodic boundary or lacked a physical boundary. The new concept of ultra chaos provides a plausible explanation as to why space debris can spread to a vast area, as most pieces of debris have a displaced COM.