Patent ID: 8282043

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 first set of firing commands for the thrusters from solutions to momentum dumping and drift control equations; and firing the thrusters according to the first set of firing commands, wherein the momentum dumping and drift control equations for the first set of firing commands are defined as Δ ⁢ ⁢ H ⇀ = ∑ i ⁢ r ⇀ i ⊗ f ⇀ i ⁢ Δ ⁢ ⁢ t i ∑ i ⁢ f i tangential ⁢ Δ ⁢ ⁢ t i = Δ ⁢ ⁢ P Drift ; where Δ{right arrow over (H)}=momentum dumping requirement (vector) in orbit frame ΔP Drift =spacecraft mass×minimum delta velocity required to control mean Drift {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 C Orbit to ECI =transformation matrix from orbit to ECI frame 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 ] and wherein the method further comprises the step of: generating a second set of firing commands for the thrusters from solutions to momentum dumping/drift and eccentricity control equations, wherein the momentum dumping/drift and eccentricity control equations are defined as P tangential = ∑ i ⁢ f i tangential ⁢ Δ ⁢ ⁢ t i P radial = ∑ i ⁢ f i tangential ⁢ Δ ⁢ ⁢ t i λ Eccentricity = tan - 1 ⁡ ( 2 ⁢ ⁢ P tangential ⁢ Δ ⁢ ⁢ P H 1 + P radial ⁢ Δ ⁢ ⁢ V K 1 2 ⁢ ⁢ P tangential ⁢ Δ ⁢ ⁢ P K 1 - P radial ⁢ Δ ⁢ ⁢ V H 1 ) Δ ⁢ ⁢ H ⇀ ECI = C Orbit ⁢ ⁢ to ⁢ ⁢ ECI ⁢ Δ ⁢ ⁢ H ⇀ Δ ⁢ ⁢ H ⇀ = ∑ i ⁢ r ⇀ i ⊗ f ⇀ i ⁢ Δ ⁢ ⁢ t i ∑ i ⁢ f i tangential ⁢ Δ ⁢ ⁢ t i = Δ ⁢ ⁢ P Drift ; where {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 1 =spacecraft mass×minimum delta velocity required to control mean K 1 ΔP H 1 =spacecraft mass×minimum delta velocity required to control mean H 1 ΔP Drift =spacecraft mass×minimum delta velocity required to control mean Drift {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 Eccentricity =location of the maneuver C Orbit to ECI =transformation matrix from orbit to ECI frame, rotation matrix about the Z by λ Eccentricity 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 ] .