Abstract: Based on Lawden equation, a new form of state transfer matrixes was presented. The state transfer matrix was derived in terms of position-velocity in solid space, and transformed from angle domain to time domain, so the state transfer matrix denoting true position and velocity was obtained. Arbitrary forms can be obtained by primary transformation. The numerical simulations show this state transfer matrix is effective and feasible for theory and project applications. It can be used for solid orbit rendezvous, orbit correction, formation configuration design and control for elliptic orbits with arbitrary eccentricity.

Key words: State-transition matrix, Time domain, Rendezvous, Relative dynamics, Elliptical orbit, Formation flight, Spacecraft