。=2my-Nm m se da= aim [2v"-j2V-Vndv N 2VT-(Vr-VN) 2 +2 2×2 Now i_4 2 =2×26/) 9 define r V d,(e-wp(w2+22) dn=1-R为 1+2R 16.522, Space P pessan Lecture Prof. Manuel martinez Page 7 of16.522, Space Propulsion Lecture 15 Prof. Manuel Martinez-Sanchez Page 7 of 11 N i T T N i 2eV i m v 0 i d 2eV v N i N m 0 i m- vdv e m v dv d= = 2jm 2ev 2je v-v v - e m ε ⎛ ⎞ ⎜ ⎟ ε ⎝ ⎠ ∫ ∫ N 2d v - v ( ) T T N N v v 0i 0i d N N TN T TN v v m m 4 d = 2v v - v - 2 v - v dv = v - v 2v - v - v 2je 2je 3 ε ε ⎧ ⎫ ⎪ ⎪ ⎛ ⎞ ⎡ ⎤ ⎨ ⎬ ⎜ ⎟ ⎣ ⎦ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭ ∫ ( ) T N v 3 2 N v 4 v-v 3 T N 2 4 v+ v 3 3 ( ) 0 i d T NT N 2 m d = v - v v + 2v 3 ej ε ( ) 1 1 4 4 1 11 1 0 2 22 2 d T NT N i 2×2 e d = V - V V + 2V 3 jm ε ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ Now 3 2 T 0 2 i a 42 e V j = 9 m d ε , so 1 3 4 4 1 1 4 2 T a 0 1 2 i 2 e V d = ×2 3 m j ⎛ ⎞ ε ⎜ ⎟ ⎝ ⎠ define N T V R = V ( ) ( ) 1 12 12 12 12 2 TN T T d 3 4 a T d V - V V + 2V = d V ( ) ( ) 1 1 1 2 d 2 2 a d = 1 - R 1+ 2R d