"""
Maximum ΔV that a spacecraft can impulse for a given single time step
"""
function max_ΔV(duty_cycle::Float64,
                num_thrusters::Int,
                max_thrust::Float64,
                tf::Float64,
                t0::Float64,
                mass::Float64)
  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_unit::Vector{Float64},
                  state::Vector{Float64},
                  duty_cycle::Float64,
                  num_thrusters::Int,
                  max_thrust::Float64,
                  mass::Float64,
                  mass_flow_rate::Float64,
                  μ::Float64,
                  time::Float64)

  if norm(ΔV_unit) > 1.
    throw(ErrorException("ΔV input is too high"))
  end
  halfway = laguerre_conway(state, μ, time/2)
  halfway[4:6] += ΔV_unit * max_ΔV(duty_cycle, num_thrusters, max_thrust, time, 0., mass)
  return laguerre_conway(halfway, μ, time/2), mass - mass_flow_rate*norm(ΔV_unit)*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{Float64},
                  state::Vector{Float64},
                  craft::Sc,
                  μ::Float64,
                  time::Float64)
  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(ΔV_units::Vector{Vector{Float64}},
              state::Vector{Float64},
              duty_cycle::Float64,
              num_thrusters::Int,
              max_thrust::Float64,
              mass::Float64,
              mass_flow_rate::Float64,
              μ::Float64,
              time::Float64,
              n::Int)

  if length(ΔV_units) != n
    throw(ExceptionError("Bad number of ΔV vectors"))
  end

  for i in 1:n
    state, mass = prop_one(ΔV_units[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(ΔV_units::Vector{Vector{Float64}},
              state::Vector{Float64},
              craft::Sc,
              μ::Float64,
              time::Float64,
              n::Int)

  if length(ΔV_units) != n
    throw(ExceptionError("Bad number of ΔV vectors"))
  end

  states = state'
  masses = craft.mass

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

  return states, masses

end