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Reentry velocity of lunar module reaches the second cosmic velocity, which could make the aerodynamic environment insupportable. So it is essential to analysis the reentry aerodynamic load. The equation of motion for reentry vehicle is a group of ordinary differential equations, and numerical methods are inadequate for online mission because their computation amount is too large. An analytical method of solving the reentry equation of motion is proposed in this paper to analyze the reentry aerodynamic load. First, matched asymptotic method is used to obtain solutions of longitudinal equation of motion in outer and inner region independently and combine them to obtain a unified closed-form solution. Reentry aerodynamic load has been analyzed in three fragments using the closed-form solution, and approximate solution of load is compared with the exact solution. Second, suppositional initial conditions are obtained by solving the closed-form solution using current state, then an analytical method of predicting the first load peak is proposed, and the relative prediction error is analyzed for different bank angles. Third, the load relief method based on load peak prediction is proposed, which can redistribute the total dissipated energy in the whole reentry process, and the validity of the method is verified by Monte Carlo simulation.
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Keywords:
- reentry aerodynamic load /
- matched asymptotic expansion /
- closed-form approximate solution /
- load relief
[1] Bairstow S H 2006 Ph. D. Dissertation (Massachusetts: Massachusetts Institute of Techlonogy)
[2] Hwang I, Li J, Du D 2009 J. Dyn. Sys. Meas. Control. 131 051010
[3] Wu H B, Zhang Y F, Mei F X 2006 Acta Phys. Sin. 55 4987 (in Chinese) [吴惠彬, 张永发, 梅凤翔 2006 物理学报 55 4987]
[4] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese) [张睿超, 王连海, 岳成庆 2007 物理学报 56 3050]
[5] Hereman W, Banerjee P, Korpel A 1986 J. Phys. A 19 19
[6] Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A 26 6027
[7] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[8] Hereman W, Takaota M 1990 J. Phys. A 23 4805
[9] Panigrahi M, Dash P C 1999 Phys. Lett. A 261 284
[10] Li Z B, Pan S Q 2001 Acta Phys. Sin. 50 402 (in Chinese) [李志斌, 潘素起 2001 物理学报 50 402]
[11] Zhao H Y 1997 Reentry Dynamics and Guidance (Changsha: National University of Defense Technology Press) p114 (in Chinese) [赵汉元 1997 飞行器再入动力学和制导 (长沙: 国防科技大学出版社) 第114页]
[12] Loh W H 1965 AIAA J. 3 1688
[13] Mititelu G 2009 Celest. Mech. Dyn. Astr. 103 327
[14] Gorbonos D, Kol B 2005 Class. Quantum. Grav. 22 3935
[15] Burke W L 1971 J. Math. Phys. 12 401
[16] Gorbonos D, Kol B 2004 J. High Energy Phys. 2004 53
[17] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[18] Shi Y Y, Pottsepp L, Eckstein M C 1970 AIAA J. 9 736
[19] Vinh N X, Kuo Z S 1996 1996 AIAA/AAS Astrodynamics Conference, San Diego, America, July 29-31, 1996 p212
[20] Kluever C A 2008 J. Guidance. 31 1531
[21] Mease K D, McCreary F A 1985 12th Atmospheric Flight Mechanics Conference Snowmass, America, August 19-21, 1985 p408
[22] Lu P 2008 J. Guidance. 31 1067
[23] Shen H X, Zhou J P, Peng Q B, Li H Y 2012 Sci. China Tech. Sci. 55 2561
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[1] Bairstow S H 2006 Ph. D. Dissertation (Massachusetts: Massachusetts Institute of Techlonogy)
[2] Hwang I, Li J, Du D 2009 J. Dyn. Sys. Meas. Control. 131 051010
[3] Wu H B, Zhang Y F, Mei F X 2006 Acta Phys. Sin. 55 4987 (in Chinese) [吴惠彬, 张永发, 梅凤翔 2006 物理学报 55 4987]
[4] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese) [张睿超, 王连海, 岳成庆 2007 物理学报 56 3050]
[5] Hereman W, Banerjee P, Korpel A 1986 J. Phys. A 19 19
[6] Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A 26 6027
[7] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[8] Hereman W, Takaota M 1990 J. Phys. A 23 4805
[9] Panigrahi M, Dash P C 1999 Phys. Lett. A 261 284
[10] Li Z B, Pan S Q 2001 Acta Phys. Sin. 50 402 (in Chinese) [李志斌, 潘素起 2001 物理学报 50 402]
[11] Zhao H Y 1997 Reentry Dynamics and Guidance (Changsha: National University of Defense Technology Press) p114 (in Chinese) [赵汉元 1997 飞行器再入动力学和制导 (长沙: 国防科技大学出版社) 第114页]
[12] Loh W H 1965 AIAA J. 3 1688
[13] Mititelu G 2009 Celest. Mech. Dyn. Astr. 103 327
[14] Gorbonos D, Kol B 2005 Class. Quantum. Grav. 22 3935
[15] Burke W L 1971 J. Math. Phys. 12 401
[16] Gorbonos D, Kol B 2004 J. High Energy Phys. 2004 53
[17] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[18] Shi Y Y, Pottsepp L, Eckstein M C 1970 AIAA J. 9 736
[19] Vinh N X, Kuo Z S 1996 1996 AIAA/AAS Astrodynamics Conference, San Diego, America, July 29-31, 1996 p212
[20] Kluever C A 2008 J. Guidance. 31 1531
[21] Mease K D, McCreary F A 1985 12th Atmospheric Flight Mechanics Conference Snowmass, America, August 19-21, 1985 p408
[22] Lu P 2008 J. Guidance. 31 1067
[23] Shen H X, Zhou J P, Peng Q B, Li H Y 2012 Sci. China Tech. Sci. 55 2561
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