With heavy reusable launch vehicles becoming a key technology for low-cost and high-frequency space exploration, cable-net recovery schemes have attracted considerable attention due to their strong adaptability to landing dispersion and attitude deviations. However, under multiple sources of interference—including engine plume impingement, trolley motion, and flexible vibrations—the dynamic state information of the flexible cable-net recovery system is difficult to acquire directly, severely constraining the accuracy of closed-loop control and capture reliability. Although Kalman filtering combined with multibody dynamics models can achieve state estimation for complex systems, the flexible cable-net system is inherently a high-dimensional, nonlinear, strongly rigid-flexible coupled constrained multibody system, whose dynamic equations are formulated as index-3 differential-algebraic equations (DAEs). Conventional methods require the conversion of DAEs into ordinary differential equations (ODEs) followed by linearization, a process that is complex and lacks generality; conventional numerical integration methods converge slowly when dealing with such stiff problems, with the Jacobian matrix becoming severely ill-conditioned under large time steps and constraints being prone to violation. Therefore, developing a filtering method that does not require model transformation, can directly utilize the multibody DAE for state prediction, and can maintain constraint satisfaction has become a key technical challenge for state estimation in flexible cable-net recovery.

Large-scale studies across the Nature journals create one of the world’s most comprehensive single-cell atlases of Alzheimer’s disease and related neuropsychiatric conditions

Due to its unique orbital characteristics, the retrograde geosynchronous orbit (RGSO) has demonstrated substantial potential in the fields of space surveillance and space situational awareness. However, constrained by the direction of Earth's rotation and the tracking, telemetry, and control capabilities of launch sites, the direct launch of satellites into RGSO from Earth must overcome an additional velocity increment of more than approximately 4 km/s, entailing enormous fuel consumption and significant engineering difficulty. Conventional approaches employ lunar gravity assists to transfer from low Earth orbit or geosynchronous transfer orbit to RGSO, yet the velocity increment requirements remain relatively high and the transfer paths are limited. With the increasing development of cislunar space in recent years, an increasing number of spacecraft on cislunar orbits are being launched and deployed. If a spacecraft is placed on standby in cislunar orbits, whether the sensitive dynamical characteristics of the three-body problem in cislunar space can be exploited to achieve low-energy transfer to RGSO has become a key issue for expanding the utilization value of cislunar space assets.