Patent ID: 7918420

Claim:
A method of simultaneous orbit control and momentum dumping in a spacecraft, the spacecraft including a plurality of thrusters, the method comprising the steps of: generating a set of firing commands for the thrusters from solutions to momentum dumping and inclination control equations; and firing the thrusters according to the firing commands; wherein the momentum dumping and inclination control equations are defined as Δ ⁢ ⁢ P K 2 2 + Δ ⁢ ⁢ P H 2 2 = Δ ⁢ ⁢ P I λ Inclination = a ⁢ ⁢ tan ⁢ ⁢ 2 ⁢ ( Δ ⁢ ⁢ P H 2 Δ ⁢ ⁢ P I , Δ ⁢ ⁢ P K 2 Δ ⁢ ⁢ P I ) Δ ⁢ ⁢ H ⇀ ECI = C Orbit ⁢ ⁢ to ⁢ ⁢ ECI ⁢ Δ ⁢ ⁢ H ⇀ Δ ⁢ ⁢ H ⇀ = ∑ i ⁢ r ⇀ i ⊗ f ⇀ i ⁢ Δ ⁢ ⁢ t i ∑ i ⁢ f i normal ⁢ Δ ⁢ ⁢ t i = Δ ⁢ ⁢ P I ; where Δ{right arrow over (H)}=momentum dumping requirement (vector) in orbit frame Δ{right arrow over (H)} ECI =momentum dumping requirement (vector) in Earth-Centered Inertial frame ΔP K 2 =spacecraft mass×minimum delta velocity required to control mean K 2 ΔP H 2 =spacecraft mass×minimum delta velocity required to control mean H 2 {right arrow over (R)} i =lever arm (vector) about the c.g. for the i th thruster in spacecraft body frame {right arrow over (F)} i =thrust vector for the i th thruster in spacecraft body frame Δt i =on time for the i th thruster λ Inclination =location of the maneuver C Orbit to ECI =transformation matrix from orbit to ECI frame, rotation matrix about the Z by λ Inclination C Body to Orbit =transformation matrix from spacecraft body to orbit frame {right arrow over (r)} i =C Body to Orbit {right arrow over (R)} i f ⇀ i = C Body ⁢ ⁢ to ⁢ ⁢ Orbit ⁢ ⁢ F ⇀ i = [ f i tangential f i radial f i normal ] .