"""
Maximum ΔV that a spacecraft can impulse for a given single time step
"""
function max_ΔV(duty_cycle::T,
                num_thrusters::Int,
                max_thrust::T,
                tf::T,
                t0::T,
                mass::S) where {T <: Real, S <: Real}
  return duty_cycle*num_thrusters*max_thrust*(tf-t0)/mass
end

"""
This function propagates the spacecraft forward in time 1 Sim-Flanagan step (of variable length of time),
applying a thrust in the center.
"""
function prop_one(ΔV::Vector{T},
                  state::Vector{S},
                  duty_cycle::Float64,
                  num_thrusters::Int,
                  max_thrust::Float64,
                  mass::S,
                  mass_flow_rate::Float64,
                  μ::Float64,
                  time::Float64) where {T <: Real, S <: Real}

  mag, α, β = ΔV

  # if mag > 1 || mag < 0
    # throw(ErrorException("ΔV input is too high: $mag"))
  # elseif α > π || α < -π
    # throw(ErrorException("α angle is incorrect: $α"))
  # elseif β > π/2 || β < -π/2
    # throw(ErrorException("β angle is incorrect: $β"))
  # end

  thrust_rθh = mag * [cos(β)*sin(α), cos(β)*cos(α), sin(β)]
  a,e,i,Ω,ω,ν = xyz_to_oe(state, μ)
  θ = ω+ν
  cΩ,sΩ,ci,si,cθ,sθ = cos(Ω),sin(Ω),cos(i),sin(i),cos(θ),sin(θ)
  DCM = [cΩ*cθ-sΩ*ci*sθ -cΩ*sθ-sΩ*ci*cθ sΩ*si;
  sΩ*cθ+cΩ*ci*sθ -sΩ*sθ+cΩ*ci*cθ -cΩ*si;
  si*sθ si*cθ ci]
  ΔV = DCM*thrust_rθh

  thrust = max_ΔV(duty_cycle, num_thrusters, max_thrust, time, 0., mass) * ΔV
  halfway = laguerre_conway(state, μ, time/2) + [0., 0., 0., thrust[1], thrust[2], thrust[3]]
  return laguerre_conway(halfway, μ, time/2), mass - mass_flow_rate*norm(ΔV)*time

end

"""
A convenience function for using spacecraft. Note that this function outputs a sc instead of a mass
"""
function prop_one(ΔV_unit::Vector{T},
                  state::Vector{S},
                  craft::Sc,
                  μ::Float64,
                  time::Float64) where {T <: Real,S <: Real}
  state, mass =  prop_one(ΔV_unit, state, craft.duty_cycle, craft.num_thrusters, craft.max_thrust,
                          craft.mass, craft.mass_flow_rate, μ, time)
  return state, Sc(mass, craft.mass_flow_rate, craft.max_thrust, craft.num_thrusters, craft.duty_cycle)
end

"""
This propagates over a given time period, with a certain number of intermediate steps
"""
function prop(ΔVs::Matrix{T},
              state::Vector{Float64},
              duty_cycle::Float64,
              num_thrusters::Int,
              max_thrust::Float64,
              mass::Float64,
              mass_flow_rate::Float64,
              μ::Float64,
              time::Float64) where T <: Real

  if size(ΔVs)[2] != 3 throw(ErrorException("ΔV input is wrong size")) end
  n = size(ΔVs)[i]

  for i in 1:n
    state, mass = prop_one(ΔVs[i,:], state, duty_cycle, num_thrusters, max_thrust, mass,
                           mass_flow_rate, μ, time/n)
  end

  return state, mass

end

"""
The same function, using Scs
"""
function prop(ΔVs::AbstractArray{T},
              state::Vector{Float64},
              craft::Sc,
              μ::Float64,
              time::Float64) where T <: Real

  if size(ΔVs)[2] != 3 throw(ErrorException("ΔV input is wrong size")) end
  n = size(ΔVs)[1]

  states = state'
  masses = craft.mass

  for i in 1:n
    state, craft = prop_one(ΔVs[i,:], state, craft, μ, time/n)
    states = [states; state']
    masses = [masses, craft.mass]
  end

  return states, masses

end