Optimal Continuous/Impulsive Control for Lorentz-Augmented Spacecraft Formations

a = semimajor axis b = magnetic field vector e = eccentricity e = orbital element vector e · = matrix exponential f = true anomaly h = angular momentum magnitude i = inclination J = cost Jn = nth zonal harmonic coefficient M = mean anomaly m = mass m = magnetic dipole vector N − 1 = number of thrusts n = mean motion p = semilatus rectum q = electrical charge r = orbit radius magnitude r = position vector t = time u = continuous input/control vector v = velocity vector W = controllability Gramian ΔV = delta-v magnitude δ t = Dirac delta function ζ = differential element error λ = continuous co-state vector μ = gravitational parameter ν = discrete co-state vector ω = angular velocity vector Φ = state transition matrix Ω = right ascension of ascending node Hc∕d = continuous/discrete Hamiltonian · × = skew symmetric matrix operator Subscripts