temporary point on the inner loop wrapper
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Connor
232
julia/src/inner_loop/propagator.jl
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232
julia/src/inner_loop/propagator.jl
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export prop
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"""
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Maximum ΔV that a spacecraft can impulse for a given single time step
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"""
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function max_ΔV(duty_cycle::T,
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num_thrusters::Int,
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max_thrust::T,
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tf::T,
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t0::T,
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mass::S) where {T <: Real, S <: Real}
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return duty_cycle*num_thrusters*max_thrust*(tf-t0)/mass
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end
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"""
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This function propagates the spacecraft forward in time 1 Sim-Flanagan step (of variable length of time),
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applying a thrust in the center.
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"""
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function prop_one(thrust_unit::Vector{<:Real},
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state::Vector{<:Real},
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duty_cycle::Float64,
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num_thrusters::Int,
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max_thrust::Float64,
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mass::T,
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mass_flow_rate::Float64,
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μ::Float64,
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time::Float64) where T<:Real
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ΔV = max_ΔV(duty_cycle, num_thrusters, max_thrust, time, 0., mass) * thrust_unit
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halfway = laguerre_conway(state, μ, time/2) + [0., 0., 0., ΔV...]
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return laguerre_conway(halfway, μ, time/2), mass - mass_flow_rate*norm(thrust_unit)*time
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end
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"""
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A convenience function for using spacecraft. Note that this function outputs a sc instead of a mass
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"""
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function prop_one(ΔV_unit::Vector{T},
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state::Vector{S},
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craft::Sc,
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μ::Float64,
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time::Float64) where {T <: Real,S <: Real}
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state, mass = prop_one(ΔV_unit, state, craft.duty_cycle, craft.num_thrusters, craft.max_thrust,
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craft.mass, craft.mass_flow_rate, μ, time)
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return state, Sc(mass, craft.mass_flow_rate, craft.max_thrust, craft.num_thrusters, craft.duty_cycle)
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end
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"""
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This propagates over a given time period, with a certain number of intermediate steps
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"""
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function prop(ΔVs::Matrix{T},
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state::Vector{Float64},
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duty_cycle::Float64,
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num_thrusters::Int,
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max_thrust::Float64,
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mass::Float64,
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mass_flow_rate::Float64,
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μ::Float64,
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time::Float64) where T <: Real
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if size(ΔVs)[2] != 3 throw(ErrorException("ΔV input is wrong size")) end
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n = size(ΔVs)[i]
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for i in 1:n
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state, mass = prop_one(ΔVs[i,:], state, duty_cycle, num_thrusters, max_thrust, mass,
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mass_flow_rate, μ, time/n)
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end
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return state, mass
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end
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"""
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The same function, using Scs
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"""
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function prop(ΔVs::Matrix{T},
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state::Vector{S},
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craft::Sc,
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μ::Float64,
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time::Float64) where {T <: Real, S <: Real}
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if size(ΔVs)[2] != 3 throw(ErrorException("ΔV input is wrong size")) end
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n = size(ΔVs)[1]
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x_states = [state[1]]
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y_states = [state[2]]
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z_states = [state[3]]
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dx_states = [state[4]]
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dy_states = [state[5]]
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dz_states = [state[6]]
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masses = [craft.mass]
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for i in 1:n
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state, craft = prop_one(ΔVs[i,:], state, craft, μ, time/n)
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push!(x_states, state[1])
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push!(y_states, state[2])
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push!(z_states, state[3])
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push!(dx_states, state[4])
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push!(dy_states, state[5])
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push!(dz_states, state[6])
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push!(masses, craft.mass)
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end
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return [x_states, y_states, z_states, dx_states, dy_states, dz_states], masses, state
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end
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function prop_nlsolve(ΔVs::Matrix{T},
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state::Vector{S},
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craft::Sc,
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μ::Float64,
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time::Float64) where {T <: Real, S <: Real}
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n = size(ΔVs)[1]
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for i in 1:n
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state, craft = prop_one(ΔVs[i,:], state, craft, μ, time/n)
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end
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return state
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end
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function prop_simple(ΔVs::AbstractMatrix,
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state::AbstractVector,
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craft::Sc,
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μ::Float64,
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time::Float64)
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if size(ΔVs)[2] != 3 throw(ErrorException("ΔV input is wrong size")) end
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n = size(ΔVs)[1]
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for i in 1:n
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state, craft = prop_one(ΔVs[i,:], state, craft, μ, time/n)
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end
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return state
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end
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function prop_one_simple(Tx, Ty, Tz, x, y, z, dx, dy, dz, t, μ)
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# perform laguerre_conway once
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r0_mag = √(x^2 + y^2 + z^2)
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v0_mag = √(dx^2 + dy^2 + dz^2)
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σ0 = ([x, y, z] ⋅ [dx, dy, dz])/√(μ)
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a = 1 / ( 2/r0_mag - v0_mag^2/μ )
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coeff = 1 - r0_mag/a
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if a > 0 # Elliptical
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ΔM = ΔE_new = √(μ) / sqrt(a^3) * t/2
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ΔE = 1000
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while abs(ΔE - ΔE_new) > 1e-10
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ΔE = ΔE_new
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F = ΔE - ΔM + σ0 / √(a) * (1-cos(ΔE)) - coeff * sin(ΔE)
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dF = 1 + σ0 / √(a) * sin(ΔE) - coeff * cos(ΔE)
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d2F = σ0 / √(a) * cos(ΔE) + coeff * sin(ΔE)
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sign = dF >= 0 ? 1 : -1
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ΔE_new = ΔE - 5*F / ( dF + sign * √(abs((5-1)^2*dF^2 - 5*(5-1)*F*d2F )))
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end
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F = 1 - a/r0_mag * (1-cos(ΔE))
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G = a * σ0/ √(μ) * (1-cos(ΔE)) + r0_mag * √(a) / √(μ) * sin(ΔE)
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r = a + (r0_mag - a) * cos(ΔE) + σ0 * √(a) * sin(ΔE)
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Ft = -√(a)*√(μ) / (r*r0_mag) * sin(ΔE)
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Gt = 1 - a/r * (1-cos(ΔE))
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else # Hyperbolic or Parabolic
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ΔN = √(μ) / sqrt(-a^3) * t/2
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ΔH = 0
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ΔH_new = t/2 < 0 ? -1 : 1
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while abs(ΔH - ΔH_new) > 1e-10
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ΔH = ΔH_new
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F = -ΔN - ΔH + σ0 / √(-a) * (cos(ΔH)-1) + coeff * sin(ΔH)
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dF = -1 + σ0 / √(-a) * sin(ΔH) + coeff * cos(ΔH)
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d2F = σ0 / √(-a) * cos(ΔH) + coeff * sin(ΔH)
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sign = dF >= 0 ? 1 : -1
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ΔH_new = ΔH - 5*F / ( dF + sign * √(abs((5-1)^2*dF^2 - 5*(5-1)*F*d2F )))
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end
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F = 1 - a/r0_mag * (1-cos(ΔH))
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G = a * σ0/ √(μ) * (1-cos(ΔH)) + r0_mag * √(-a) / √(μ) * sin(ΔH)
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r = a + (r0_mag - a) * cos(ΔH) + σ0 * √(-a) * sin(ΔH)
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Ft = -√(-a)*√(μ) / (r*r0_mag) * sin(ΔH)
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Gt = 1 - a/r * (1-cos(ΔH))
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end
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# add the thrust vector
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x,y,z,dx,dy,dz = [F*[x,y,z] + G*[dx,dy,dz]; Ft*[x,y,z] + Gt*[dx,dy,dz] + [Tx, Ty, Tz]]
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#perform again
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r0_mag = √(x^2 + y^2 + z^2)
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v0_mag = √(dx^2 + dy^2 + dz^2)
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σ0 = ([x, y, z] ⋅ [dx, dy, dz])/√(μ)
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a = 1 / ( 2/r0_mag - v0_mag^2/μ )
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coeff = 1 - r0_mag/a
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if a > 0 # Elliptical
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ΔM = ΔE_new = √(μ) / sqrt(a^3) * t/2
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ΔE = 1000
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while abs(ΔE - ΔE_new) > 1e-10
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ΔE = ΔE_new
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F = ΔE - ΔM + σ0 / √(a) * (1-cos(ΔE)) - coeff * sin(ΔE)
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dF = 1 + σ0 / √(a) * sin(ΔE) - coeff * cos(ΔE)
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d2F = σ0 / √(a) * cos(ΔE) + coeff * sin(ΔE)
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sign = dF >= 0 ? 1 : -1
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ΔE_new = ΔE - 5*F / ( dF + sign * √(abs((5-1)^2*dF^2 - 5*(5-1)*F*d2F )))
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end
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F = 1 - a/r0_mag * (1-cos(ΔE))
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G = a * σ0/ √(μ) * (1-cos(ΔE)) + r0_mag * √(a) / √(μ) * sin(ΔE)
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r = a + (r0_mag - a) * cos(ΔE) + σ0 * √(a) * sin(ΔE)
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Ft = -√(a)*√(μ) / (r*r0_mag) * sin(ΔE)
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Gt = 1 - a/r * (1-cos(ΔE))
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else # Hyperbolic or Parabolic
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ΔN = √(μ) / sqrt(-a^3) * t/2
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ΔH = 0
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ΔH_new = t/2 < 0 ? -1 : 1
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while abs(ΔH - ΔH_new) > 1e-10
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ΔH = ΔH_new
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F = -ΔN - ΔH + σ0 / √(-a) * (cos(ΔH)-1) + coeff * sin(ΔH)
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dF = -1 + σ0 / √(-a) * sin(ΔH) + coeff * cos(ΔH)
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d2F = σ0 / √(-a) * cos(ΔH) + coeff * sin(ΔH)
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sign = dF >= 0 ? 1 : -1
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ΔH_new = ΔH - 5*F / ( dF + sign * √(abs((5-1)^2*dF^2 - 5*(5-1)*F*d2F )))
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end
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F = 1 - a/r0_mag * (1-cos(ΔH))
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G = a * σ0/ √(μ) * (1-cos(ΔH)) + r0_mag * √(-a) / √(μ) * sin(ΔH)
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r = a + (r0_mag - a) * cos(ΔH) + σ0 * √(-a) * sin(ΔH)
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Ft = -√(-a)*√(μ) / (r*r0_mag) * sin(ΔH)
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Gt = 1 - a/r * (1-cos(ΔH))
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end
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return [F*[x,y,z] + G*[dx,dy,dz]; Ft*[x,y,z] + Gt*[dx,dy,dz]]
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end
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