142 lines
3.6 KiB
Julia
142 lines
3.6 KiB
Julia
export oe_to_rθh, rθh_to_xyz, oe_to_xyz, xyz_to_oe, conv_T, spiral, gen_orbit
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function oe_to_rθh(oe::Vector,μ::Real) :: Vector
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a,e,i,Ω,ω,ν = oe
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return [a*(1-e^2)/(1+e*cos(ν)),
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0,
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0,
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(μ/sqrt(μ*a*(1-e^2)))*e*sin(ν),
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(μ/sqrt(μ*a*(1-e^2)))*(1+e*cos(ν)),
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0]
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end
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function rθh_to_xyz(rθh_vec::Vector,oe::Vector)
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a,e,i,Ω,ω,ν = oe
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θ = ω+ν
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cΩ,sΩ,ci,si,cθ,sθ = cos(Ω),sin(Ω),cos(i),sin(i),cos(θ),sin(θ)
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DCM = [cΩ*cθ-sΩ*ci*sθ -cΩ*sθ-sΩ*ci*cθ sΩ*si;
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sΩ*cθ+cΩ*ci*sθ -sΩ*sθ+cΩ*ci*cθ -cΩ*si;
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si*sθ si*cθ ci]
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DCM = kron(Matrix(I,2,2),DCM)
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return DCM*rθh_vec
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end
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function oe_to_xyz(oe::Vector,μ::Real)
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return rθh_to_xyz(oe_to_rθh(oe,μ),oe)
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end
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function xyz_to_oe(cart_vec::Vector,μ::Real)
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r_xyz, v_xyz = cart_vec[1:3],cart_vec[4:6]
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r = norm(r_xyz)
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h_xyz = cross(r_xyz,v_xyz) #km^2/s
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h = norm(h_xyz) #km^2/s
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ξ = dot(v_xyz,v_xyz)/2 - μ/r #km^2 s^-2
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a = -μ/(2ξ) #km
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e_xyz = cross(v_xyz,h_xyz)/μ - r_xyz/r
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e = norm(e_xyz)
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if h_xyz[3]/h < 1.
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i = acos(h_xyz[3]/h) #rad
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else
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i = acos(1.)
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end
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n_xyz = cross([0,0,1],h_xyz)
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if dot(n_xyz,[1,0,0])/norm(n_xyz) < 1.
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Ω = acos(dot(n_xyz,[1,0,0])/norm(n_xyz))
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else
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Ω = acos(1.)
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end
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if dot(n_xyz,e_xyz)/(norm(n_xyz)*e) < 1.
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ω = acos(dot(n_xyz,e_xyz)/(norm(n_xyz)*e))
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else
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ω = acos(1.)
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end
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if abs((dot(r_xyz,e_xyz))/(r*norm(e_xyz))) < 1.
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ν = acos((dot(r_xyz,e_xyz))/(r*norm(e_xyz)))
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else
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ν = acos(1.)
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end
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Ω = dot(n_xyz,[0,1,0]) > 0. ? Ω : -Ω
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ω = dot(e_xyz,[0,0,1]) > 0. ? ω : -ω
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ν = dot(r_xyz,v_xyz) > 0. ? ν : -ν
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return [a,e,i,Ω,ω,ν]
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end
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"""
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A convenience function for generating start conditions from orbital elements
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Inputs: a body, a period, and a mass
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Output: a random reasonable orbit
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"""
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function gen_orbit(T::Float64, mass::Float64, primary::Body=Sun)
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μ = primary.μ
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i = rand(0.0:0.01:0.4999π)
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θ = rand(0.0:0.01:2π)
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i = 0
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while true
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i += 1
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e = rand(0.0:0.01:0.5)
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a = ∛(μ * ( T/2π )^2 )
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a*(1-e) < 1.1primary.r || return [ oe_to_xyz([ a, e, i, 0., 0., θ ], μ); mass ]
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i < 100 || throw(GenOrbit_Error)
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end
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end
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"""
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A convenience function for generating spiral trajectories
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"""
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spiral(mag,n,init,sc,time,primary=Sun) = conv_T(fill(mag, n), zeros(n), zeros(n), init, sc, time, primary)
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"""
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Converts a series of thrust vectors from R,Θ,H frame to cartesian
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"""
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function conv_T(Tm::Vector{Float64},
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Ta::Vector{Float64},
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Tb::Vector{Float64},
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init_state::Vector{Float64},
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craft::Sc,
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time::Float64,
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primary::Body=Sun)
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Txs = Float64[]
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Tys = Float64[]
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Tzs = Float64[]
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n::Int = length(Tm)
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for i in 1:n
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mag, α, β = Tm[i], Ta[i], Tb[i]
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if mag > 1 || mag < 0
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@error "ΔV input is too high: $mag"
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elseif α > π || α < -π
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@error "α angle is incorrect: $α"
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elseif β > π/2 || β < -π/2
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@error "β angle is incorrect: $β"
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end
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end
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state = init_state
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for i in 1:n
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mag, α, β = Tm[i], Ta[i], Tb[i]
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thrust_rθh = mag * [cos(β)*sin(α), cos(β)*cos(α), sin(β)]
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_,_,i,Ω,ω,ν = xyz_to_oe(state, primary.μ)
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θ = ω+ν
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cΩ,sΩ,ci,si,cθ,sθ = cos(Ω),sin(Ω),cos(i),sin(i),cos(θ),sin(θ)
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DCM = [cΩ*cθ-sΩ*ci*sθ -cΩ*sθ-sΩ*ci*cθ sΩ*si;
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sΩ*cθ+cΩ*ci*sθ -sΩ*sθ+cΩ*ci*cθ -cΩ*si;
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si*sθ si*cθ ci ]
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Tx, Ty, Tz = DCM*thrust_rθh
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state = prop_one([Tx, Ty, Tz], state, craft, time/n, primary)
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push!(Txs, Tx)
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push!(Tys, Ty)
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push!(Tzs, Tz)
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end
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return hcat(Txs, Tys, Tzs)
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end
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