Terminal Conditions(Multi-Spacecrafyrnk For each spacecraft (Ro projection on y-z plane) 300 c Position Conditions c xsiny+ =COSY R (5/2] siny m2 =xcosy-2sIny Velocity Conditions 100 y_xsin+=cosy np/x (5/2川 InR siny」 m4 =xcosy-2siny 30902001000 00200300 Where Velocity Vector (m) · Tying Condition ms=j(xsiny +coSY C=√2R∑ vI-cos 0 for j=1.2.N-1 ylrsiny+EcosY)+anR siny 4 spacecraft example C1=435C2=342C3=167 Phasing Condition(Cluster) N-th Condition(Total of 6N conditions) ∑ 6N-1 p(1)=∑d4(x(t) Space Systems Laboratory Massachusetts Institute of TechnologySpace Systems Laboratory Massachusetts Institute of Technology Terminal Conditions (Multi Terminal Conditions (Multi-Spacecraft) Spacecraft) Phasing Condition (Cluster): 2 1 , c o s N i o i j j i C R = = ∑ − θ 5 N N i i j i i j y y m C z z + = ⎡ ⎤ ⎡ ⎤ = − − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ∑ ( ) = γ − γ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ γ γ + γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = cos sin 1 5 / 2 sin sin cos 2 2 2 1 m x z R x z R y m o o ( ) = γ − γ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ γ γ + γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = cos sin 1 5 / 2 sin sin cos 4 2 2 3 m x z nR x z nR y m o o & & & & & For each spacecraft ( R o projection on y-z plane): • Position Conditions • Velocity Conditions • Tying Condition = ( ) sin γ + cos γ 5 m y& x z − ( ) γ + γ + sin γ 2 5 sin cos 2 o y x& z& nR 6 1 * * 1 p ( ) d [ ( x ( ) )] x N i f i f i m t t − = ∂ − = ∂ ∑ N-th Condition (Total of 6 N conditions) for i = 1, 2, …, N-1 where 4 spacecraft example: C1 = 4.35 C 2 = 3.42 C 3 = 1.67