可重复使用飞行器再入制导方法研究
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摘要
与传统的天地往返运输系统相比,新一代可重复使用飞行器具有更高的可靠性、更低的发射成本以及更少的发射准备时间,能够实现快速、可靠、经济的进入空间的目标,因此受到世界各国的普遍关注。由于再入过程中的飞行环境异常复杂,保证飞行安全并满足任务要求的制导精度对再入制导提出了严峻的挑战。因此,需要对可重复使用飞行器的再入制导方法进行深入的研究。
本文对可重复使用飞行器的再入制导方法进行了较为深入的研究:
首先,在建立可重复使用飞行器再入模型的基础上,本文对可重复使用飞行器质心运动进行分析,提出再入制导问题,明确飞行器再入过程中的各种约束,并根据再入飞行各阶段的不同目的对轨迹进行分段。
然后,将再入制导问题分为纵向再入轨迹规划问题、纵向轨迹跟踪问题和侧向再入制导问题,给出纵向再入走廊的计算算法,并说明影响其形状的各因素。在纵向再入轨迹规划中,引入两个轨迹过渡条件,提出一种同时设计连续的参考攻角剖面与参考倾侧角剖面的规划方法,保证各段纵向参考轨迹满足约束并光滑衔接。由于纵向参考轨迹规划过程中采用近似条件造成航程损失,在线性化质心运动方程的基础上,利用LQR方法设计纵向轨迹跟踪律,通过修正并平滑参考攻角剖面与参考倾侧角剖面,使得可重复使用飞行器满足再入任务对航程的要求。在侧向制导中,本文采用一种具有较好通用性的侧向再入制导方法为RLV设计侧向再入制导律。
最后,在多种具有代表性的再入任务假定以及空气动力系数、大气密度存在偏差或扰动的情况下,通过数值仿真对本文研究的再入制导方法进行验证并给出分析和结论。数值仿真结果表明,本文研究的再入制导方法具有较好的适应性和一定的鲁棒性。该方法具有较好的应用前景。
Compared with the conventional space transportation systems, the next generation Reusable Launch Vehicles (RLVs) possess higher reliability, lower launch cost, and less turnaround time. They have the ability to achieve rapid, reliable and affordable access to space and receive considerable attentions. To ensure flight safety and guidance precision, entry guidance encounters the huge challenges resulted form the extremely complex environment in entry phase. Thus, entry guidance method for RLVs needs to be researched comprehensively.
The entry guidance method for RLV is investigated in this dissertation: First, mass-point dynamics of RLV is established and analysed. Entry guidance problem is proposed and the constraints are determined. The trajectory are divided into several parts according to the different objectives of entry guidance.
Then, entry guidance problem is decomposed into three subproblems: longitudinal trajectory planning, longitudinal trajectory tracking and lateral guidance. The algorithm for longitudinal entry corridor computation is introduced, and the factors influenced the longitudinal entry corridor are listed. In longitudinal trajectory planning subproblem, two trajectory transition criterions are introduced, and a new method focused on planning both the angle of attack profile and the bank angle profile is proposed for constraints observance and trajectory smoothness. And in view of the range deficiency resulted from the approximations introduced in longitudinal trajectory planning, a trajectory tracking law is designed via LQR theory to follow the longitudinal reference trajectory and modify angle of attack profile and bank angle profile. In lateral guidance subproblem, a lateral guidance method with good compatibility is introduced and applied to the design of lateral guidance law for RLV.
Finally, the above guidance method is demonstrated by numerical simulation under several typical entry scenarios, deflections and disturbances are taken into account.
Analyses and conclusions are given at the end of this dissertation. The results of numerical simulation indicate that the entry guidance method researched in this dissertation provides robustness to some uncertainties and has adaptability to various entry missions. It has good potential for further applications.
本文对可重复使用飞行器的再入制导方法进行了较为深入的研究:
首先,在建立可重复使用飞行器再入模型的基础上,本文对可重复使用飞行器质心运动进行分析,提出再入制导问题,明确飞行器再入过程中的各种约束,并根据再入飞行各阶段的不同目的对轨迹进行分段。
然后,将再入制导问题分为纵向再入轨迹规划问题、纵向轨迹跟踪问题和侧向再入制导问题,给出纵向再入走廊的计算算法,并说明影响其形状的各因素。在纵向再入轨迹规划中,引入两个轨迹过渡条件,提出一种同时设计连续的参考攻角剖面与参考倾侧角剖面的规划方法,保证各段纵向参考轨迹满足约束并光滑衔接。由于纵向参考轨迹规划过程中采用近似条件造成航程损失,在线性化质心运动方程的基础上,利用LQR方法设计纵向轨迹跟踪律,通过修正并平滑参考攻角剖面与参考倾侧角剖面,使得可重复使用飞行器满足再入任务对航程的要求。在侧向制导中,本文采用一种具有较好通用性的侧向再入制导方法为RLV设计侧向再入制导律。
最后,在多种具有代表性的再入任务假定以及空气动力系数、大气密度存在偏差或扰动的情况下,通过数值仿真对本文研究的再入制导方法进行验证并给出分析和结论。数值仿真结果表明,本文研究的再入制导方法具有较好的适应性和一定的鲁棒性。该方法具有较好的应用前景。
Compared with the conventional space transportation systems, the next generation Reusable Launch Vehicles (RLVs) possess higher reliability, lower launch cost, and less turnaround time. They have the ability to achieve rapid, reliable and affordable access to space and receive considerable attentions. To ensure flight safety and guidance precision, entry guidance encounters the huge challenges resulted form the extremely complex environment in entry phase. Thus, entry guidance method for RLVs needs to be researched comprehensively.
The entry guidance method for RLV is investigated in this dissertation: First, mass-point dynamics of RLV is established and analysed. Entry guidance problem is proposed and the constraints are determined. The trajectory are divided into several parts according to the different objectives of entry guidance.
Then, entry guidance problem is decomposed into three subproblems: longitudinal trajectory planning, longitudinal trajectory tracking and lateral guidance. The algorithm for longitudinal entry corridor computation is introduced, and the factors influenced the longitudinal entry corridor are listed. In longitudinal trajectory planning subproblem, two trajectory transition criterions are introduced, and a new method focused on planning both the angle of attack profile and the bank angle profile is proposed for constraints observance and trajectory smoothness. And in view of the range deficiency resulted from the approximations introduced in longitudinal trajectory planning, a trajectory tracking law is designed via LQR theory to follow the longitudinal reference trajectory and modify angle of attack profile and bank angle profile. In lateral guidance subproblem, a lateral guidance method with good compatibility is introduced and applied to the design of lateral guidance law for RLV.
Finally, the above guidance method is demonstrated by numerical simulation under several typical entry scenarios, deflections and disturbances are taken into account.
Analyses and conclusions are given at the end of this dissertation. The results of numerical simulation indicate that the entry guidance method researched in this dissertation provides robustness to some uncertainties and has adaptability to various entry missions. It has good potential for further applications.
引文
1.赵汉元.飞行器再入动力学与制导.国防科技大学出版社,1997:1-167
2.杨勇等.重复使用运载器发展趋势及特点.导弹与航天运载技术,2002(5):15-19
3. Z. Shen, P. Lu. Onboard Generation of Three-Dimensional Constraints Entry Trajectory. Journal of Guidance, Control, and Dynamics. 2003, 26(1):111-121
4.陈刚等.航天器再入制导方法研究现状与发展评述.飞行力学,2008(2):1-9
5.周以蕴.取代航天飞机的RLV计划.航天,1997(1):18-19
6.潘乐飞.可重复使用运载器再入制导研究.西北工业大学硕士学位论文,2006
7. R. C. Wingrove. Survey of Atmosphere Re-entry Guidance and Control Methords. AIAA Journal. 1963(9):2019-2029
8. K. D. Mease, J. P. Kremer. Shuttle entry guidance revisited. AIAA 92-4450, 1992
9. J. C. Harpold, C. A. Graves. Shuttle entry guidance. Journal of the Astronautical Science, 1979(3):239-268
10. J. L. Speyer. Optimization and control using perturbation theory to find neighboring optimum path. SIAM symposium on multivariable linear control system theory, Boston, Mass, November 1-2, 1962.
11. R. Morth. Optimum re-entry trajectories by dynamic programming. Boeing Doc. D2-9748, April 1961.
12. A. E. Bryson, W. F. Denham, F. J. Carroll, K. Mikami. Determination of the lift or drag program that minimizes re-entry heating with acceleration or range constraints using a steepest descent computation procedure. Journal of Aerospace Science. 1962(29): 420-430
13. A. E. Bryson, K. Mikami, C. T. Battle. Optimum lateral turns for a re-entry glider. Aerospace Engineering. 1962(21), 18-23 March.
14. E. S. Levinsky. Application of inequality constraints to variational problems of lifting re-entry. Journal of Aerospace Science. 1962(29): 400-409
15. W. F. Denham, A. E. Jr. Bryson. The solution of optimal programming problems with inequality constraints. IAS Paper, 1963: 63-78
16. T. R. Jorris, C. S. Schulz, F. R. Friedl. Constrainted Trajectory Optimization Using Pseudospectral Methods. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008
17. B. Kang, S. Tang. Optimal Trajectory of Hypersonic Vehicle for Global Reach. The 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Dayton, Ohio, April 28 - May 1, 2008.
18. H. C. Lessing, P. J. Tunnell, R. E. Coate. Lunar Landing and Long-range Earth Re-entry Guidance by Application of Perturbation Theory. Proceedings of the AIAA second manned spaceflight Meeting, AIAA, New York, 1963: 140-150.
19. R. W. Spratlin. An Adaptive Numeric Predictor-Corrector Guidance Algorithm for Atmospheric Entry Vehicles. M. S. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, May 1987.
20. D. P. Fuhry.Adaptive Atmosphere Reentry Guidance for the Kistler K-1 Orbital Vehicle.AIAA 99-4211,1998
21. F. Jouhaud. Closed Loop Reentry Guidance Law of a Space Plane: Application to Hermes. Acta Astronautica,1992(8-10):577-585
22. J. M. Hanson. Advanced Guidance and Control Project for Reusable Launch Vehicles. AIAA Guidance, Navigation, and Control Conference, Denver, CO, August 14-17, 2000
23. J. M. Hanson. New Guidance for New Launchers. Aerospace America. 20031 41(3): 36-41
24. K. D. Mease, D. T. Chen, P. Teufel, H. Sch?nenberger. Reduced-Order Entry Trajectory Planning for Acceleration Guidance. Journal of Guidance, Control, and Dynamics. 2002, 25(2): 257-266
25. A. Saraf, J. A. Leavitt, D. T. Chen, K. D. Mease. Design and Evaluation of an Acceleration Guidance Algorithm for Entry. Journal of Spacecraft and Rockets. 2004, 41(6): 986-996
26. A. Saraf, J. A. Leavitt, K. D. Mease. Landing Footpoint Comnputation for Entry Vehicles. AIAA-04-4774: AIAA Guidance, Navigation, and Control Conference, Providence, RI, August 16-19, 2004.
27. J. A. Leavitt, K. D. Mease. Feasible Trajectory Generation for Atmospheric Entry Guidance. Journal of Guidance, Control, and Dynamics. 2007, 30(2): 437-481.
28. M. A. DeVirgilio, G.. R. Wells, E. E. Schiring. Optimal Guidance for Aero-dynamically Controlled Re-Entry Vehicles. AIAA Journal. 1974, 12(10)
29. A. Roenneke, A. Markl. Re-Entry Control to a Drag-vs-Energy Profile. Journal of Guidance, Control, and Dynamics. 1994, 17(5): 916-920
30. A. Roenneke, K. Well. Nonlinear Drag-Tracking Control Applied to Optimal Low-Lift Re-Entry Guidance. AIAA paper 96-3698, July, 1996.
31. P. Lu. Regulation About Time-Varying Trajectories: Precision Entry Guidance Illustrated. AIAA Guidance, Navigation, and Control Conference, Portland, OR, August 9-11, 1999
32. P. Lu, Z. Shen. Entry Guidance by Trajectory Regulation. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, CO, August 14-17, 2000
33. E. Mooij, K. D. Mease, J. Benito. Robust Re-Entry Guidance and Control SystemDesign and Analysis. AIAA Guidance, Navigation, and Control Conference and Exhibit, Hilton Head, South Carolina, August 20-23, 2007
34. T. Hormigo, J. A. Silva, F. Camara. Nonlinear Dynamic Inversion-Based Guidance and Control for a Pinpoint Mars Entry. AIAA Guidance, Navigation, and Control conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008
35. Z. Shen. On-Board Three-Dimensioonal Constraints Entry Flight Trajectory Generation. Ph. D. Thesis, Dept. of Aerospace Engineering, Iowa State University, Ames, Iowa, 2002.
36. Z. Shen, P. Lu. Onboard Entry Trajectory Planning Expanded to Sub-Orbital Flight. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, August 11-14, 2003
37. Z. Shen, P. Lu. Dynamic Lateral Entry Guidance Logic. AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island, August 16-19, 2004
38. P. Lu. Asymptotic Analysis of Quasi-Equilibrium Glide in Lifting Entry Flight. Journal of Guidance, Control, and Dynamics. 2006, 29(3).
39. J. M. Hanson, R. E. Jones. Test Result for Entry Guidance Methord for Space Vehicles. Journal of Guidance, Control, and Dynamics. 2004, 27(6): 960-966
40. P. C. Jr. Dow, D. P. Fields, F. H. Scammell. Automatic Re-Entry Guidance at Escape Velocity. ARS Preprint 1946-61, August, 1961.
41. J. P. Bryant, M. P. Frank. An Automatic Long Range Guidance System for a Cehicle Entering at Parabolic Velocity. IAS paper 62-78, June, 1962.
42. J. P. Bryant, M. P. Frank. Supercircular Re-Entry Guidance for a Fix L/D Vehicle Employing a Skip for Extreme Ranges. ARS Preprint 2489-62, 1962.
43. A Study of Energy Management Techniques for a High Lift Vehicle. General Electirc Co., Air Force Systems Command Tech. Doc. Rept. ASD-TDR-62-77, Vol. 1 and 2, June, 1962.
44. A. J. Jr. Eggers, H. J. Allen, S. E. Neice. A Comparative Anaysis of the Performance of Long-Range Hypervelocity Vehicles. NACA TR 1382, 1985; Supersedes NACA TN 4046.
45. D. R. Chapman. An Approximate Analytical methord for Studying Entry into Planetary Atmospheres. NASA TR R-11, 1959; Supersedes NACA TN 4276.
46. R. E. Slye. An Analytical Methord for Studying the Lateral Motion of Atmosphere Entry Vehicles. NASA TN D-325, 1960.
47. A. Ferri, Ting L.. Practical Aspects of Re-Entry Problems. Astronaut. Acta. 1962(VIII): 63-81
48. H. E. Wang. Approximate Solutions of the Lateral motion of Re-Entry Vehiclesduring Constant Altitude Glide. SSD-TDR-63-60, Aerospace Rept. TDR-169 (3560-10) TN-1, February 25, 1963.
49. H. Youssef, R. Chowdhry, H. Lee, P. Rodi, C. Zimmerman. Predictor-Corrector Entry Guidance for Reusable Launch Vehicles. Proceedings of AIAA Guidance, Navigation, and Control Conference, Montreal, Canada, August, 2001
50. C. Zimmerman, G.. Dukeman, J. Hanson. An Automated Method to Compute Orbital Re-Entry Trajectories with Heating Constraints. Proceedings of AIAA Guidance, Navigation, and Control Conference, Monterey, CA, August, 2002
51. G.. Dukeman. Profile-Following Entry Guidance Using Linear Quadartic Regulator Theory. Proceedings of AIAA Guidance, Navigation, and Control Conference, Monterey, CA, August, 2002
52. J. Benito, K. D. Mease. Nonlinear Predictive Controller for Drag Tracking in Entry Guidance. AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008
53. R.W. Powell. Six-Degree-of-Freedom Guidance and Control Entry Analysis of the HL-20. Journal of Spacecraft and Rockets. 1993, 30(5): 537-540
54. D. P. Fuhry. Adaptive Atmospheric Reentry Guidance for the Kistler K-1 Orbital Vehicle. Proceedings of AIAA Guidance, Navigation, and Control Conference, AIAA, Reston,VA,1999, pp:1275-1288
55. C. W. Brunner, P. Lu. Skip Emtry Trajectory Planning and Guidance. AIAA Guidance, Navigation, and Control Conference and Exhibit, Hilton Head, South Carolina, August 20-23, 2007
56. C. W. Brunner, P. Lu. Skip Emtry Trajectory Planning and Guidance. Journal of Guidance, Control and Dynamics. 2008, 31(5).
57.胡建学等. RLV再入标准轨道制导与轨道预测制导方法比较分析.国防科技大学学报, 2007(1):26-34.
58.南英等.航天器再入轨迹与控制进展.导弹与航天运载技术,1994(5):1-10.
59.李小龙,陈士橹.航天飞机的最优再入轨迹与制导.宇航学报, 1993(1):7-9.
60.南英,吕学富,陈士橹.航天器的再入走廊及其计算方法.飞行力学, 1993(2): 34-35.
61. K. J. Muephy, R. J. Nowak, R. A. Thompson, B. R. Hollis, R. K. Prabhu. X-33 Hypersonic Aerodynamic Characteristic. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Portland, Oregon, August 9-11, 1999.
62. C. Dong, S. Y. Wang, M. Yang. Research on Entry Guidance for Reusable Launch Vehicles. The 3rd International Symposium on Systems and Control in Aeronautics and Astronautics, Harbin, P. R. China, June 8-9, 2010.
2.杨勇等.重复使用运载器发展趋势及特点.导弹与航天运载技术,2002(5):15-19
3. Z. Shen, P. Lu. Onboard Generation of Three-Dimensional Constraints Entry Trajectory. Journal of Guidance, Control, and Dynamics. 2003, 26(1):111-121
4.陈刚等.航天器再入制导方法研究现状与发展评述.飞行力学,2008(2):1-9
5.周以蕴.取代航天飞机的RLV计划.航天,1997(1):18-19
6.潘乐飞.可重复使用运载器再入制导研究.西北工业大学硕士学位论文,2006
7. R. C. Wingrove. Survey of Atmosphere Re-entry Guidance and Control Methords. AIAA Journal. 1963(9):2019-2029
8. K. D. Mease, J. P. Kremer. Shuttle entry guidance revisited. AIAA 92-4450, 1992
9. J. C. Harpold, C. A. Graves. Shuttle entry guidance. Journal of the Astronautical Science, 1979(3):239-268
10. J. L. Speyer. Optimization and control using perturbation theory to find neighboring optimum path. SIAM symposium on multivariable linear control system theory, Boston, Mass, November 1-2, 1962.
11. R. Morth. Optimum re-entry trajectories by dynamic programming. Boeing Doc. D2-9748, April 1961.
12. A. E. Bryson, W. F. Denham, F. J. Carroll, K. Mikami. Determination of the lift or drag program that minimizes re-entry heating with acceleration or range constraints using a steepest descent computation procedure. Journal of Aerospace Science. 1962(29): 420-430
13. A. E. Bryson, K. Mikami, C. T. Battle. Optimum lateral turns for a re-entry glider. Aerospace Engineering. 1962(21), 18-23 March.
14. E. S. Levinsky. Application of inequality constraints to variational problems of lifting re-entry. Journal of Aerospace Science. 1962(29): 400-409
15. W. F. Denham, A. E. Jr. Bryson. The solution of optimal programming problems with inequality constraints. IAS Paper, 1963: 63-78
16. T. R. Jorris, C. S. Schulz, F. R. Friedl. Constrainted Trajectory Optimization Using Pseudospectral Methods. AIAA Atmospheric Flight Mechanics Conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008
17. B. Kang, S. Tang. Optimal Trajectory of Hypersonic Vehicle for Global Reach. The 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Dayton, Ohio, April 28 - May 1, 2008.
18. H. C. Lessing, P. J. Tunnell, R. E. Coate. Lunar Landing and Long-range Earth Re-entry Guidance by Application of Perturbation Theory. Proceedings of the AIAA second manned spaceflight Meeting, AIAA, New York, 1963: 140-150.
19. R. W. Spratlin. An Adaptive Numeric Predictor-Corrector Guidance Algorithm for Atmospheric Entry Vehicles. M. S. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, May 1987.
20. D. P. Fuhry.Adaptive Atmosphere Reentry Guidance for the Kistler K-1 Orbital Vehicle.AIAA 99-4211,1998
21. F. Jouhaud. Closed Loop Reentry Guidance Law of a Space Plane: Application to Hermes. Acta Astronautica,1992(8-10):577-585
22. J. M. Hanson. Advanced Guidance and Control Project for Reusable Launch Vehicles. AIAA Guidance, Navigation, and Control Conference, Denver, CO, August 14-17, 2000
23. J. M. Hanson. New Guidance for New Launchers. Aerospace America. 20031 41(3): 36-41
24. K. D. Mease, D. T. Chen, P. Teufel, H. Sch?nenberger. Reduced-Order Entry Trajectory Planning for Acceleration Guidance. Journal of Guidance, Control, and Dynamics. 2002, 25(2): 257-266
25. A. Saraf, J. A. Leavitt, D. T. Chen, K. D. Mease. Design and Evaluation of an Acceleration Guidance Algorithm for Entry. Journal of Spacecraft and Rockets. 2004, 41(6): 986-996
26. A. Saraf, J. A. Leavitt, K. D. Mease. Landing Footpoint Comnputation for Entry Vehicles. AIAA-04-4774: AIAA Guidance, Navigation, and Control Conference, Providence, RI, August 16-19, 2004.
27. J. A. Leavitt, K. D. Mease. Feasible Trajectory Generation for Atmospheric Entry Guidance. Journal of Guidance, Control, and Dynamics. 2007, 30(2): 437-481.
28. M. A. DeVirgilio, G.. R. Wells, E. E. Schiring. Optimal Guidance for Aero-dynamically Controlled Re-Entry Vehicles. AIAA Journal. 1974, 12(10)
29. A. Roenneke, A. Markl. Re-Entry Control to a Drag-vs-Energy Profile. Journal of Guidance, Control, and Dynamics. 1994, 17(5): 916-920
30. A. Roenneke, K. Well. Nonlinear Drag-Tracking Control Applied to Optimal Low-Lift Re-Entry Guidance. AIAA paper 96-3698, July, 1996.
31. P. Lu. Regulation About Time-Varying Trajectories: Precision Entry Guidance Illustrated. AIAA Guidance, Navigation, and Control Conference, Portland, OR, August 9-11, 1999
32. P. Lu, Z. Shen. Entry Guidance by Trajectory Regulation. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, CO, August 14-17, 2000
33. E. Mooij, K. D. Mease, J. Benito. Robust Re-Entry Guidance and Control SystemDesign and Analysis. AIAA Guidance, Navigation, and Control Conference and Exhibit, Hilton Head, South Carolina, August 20-23, 2007
34. T. Hormigo, J. A. Silva, F. Camara. Nonlinear Dynamic Inversion-Based Guidance and Control for a Pinpoint Mars Entry. AIAA Guidance, Navigation, and Control conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008
35. Z. Shen. On-Board Three-Dimensioonal Constraints Entry Flight Trajectory Generation. Ph. D. Thesis, Dept. of Aerospace Engineering, Iowa State University, Ames, Iowa, 2002.
36. Z. Shen, P. Lu. Onboard Entry Trajectory Planning Expanded to Sub-Orbital Flight. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, August 11-14, 2003
37. Z. Shen, P. Lu. Dynamic Lateral Entry Guidance Logic. AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island, August 16-19, 2004
38. P. Lu. Asymptotic Analysis of Quasi-Equilibrium Glide in Lifting Entry Flight. Journal of Guidance, Control, and Dynamics. 2006, 29(3).
39. J. M. Hanson, R. E. Jones. Test Result for Entry Guidance Methord for Space Vehicles. Journal of Guidance, Control, and Dynamics. 2004, 27(6): 960-966
40. P. C. Jr. Dow, D. P. Fields, F. H. Scammell. Automatic Re-Entry Guidance at Escape Velocity. ARS Preprint 1946-61, August, 1961.
41. J. P. Bryant, M. P. Frank. An Automatic Long Range Guidance System for a Cehicle Entering at Parabolic Velocity. IAS paper 62-78, June, 1962.
42. J. P. Bryant, M. P. Frank. Supercircular Re-Entry Guidance for a Fix L/D Vehicle Employing a Skip for Extreme Ranges. ARS Preprint 2489-62, 1962.
43. A Study of Energy Management Techniques for a High Lift Vehicle. General Electirc Co., Air Force Systems Command Tech. Doc. Rept. ASD-TDR-62-77, Vol. 1 and 2, June, 1962.
44. A. J. Jr. Eggers, H. J. Allen, S. E. Neice. A Comparative Anaysis of the Performance of Long-Range Hypervelocity Vehicles. NACA TR 1382, 1985; Supersedes NACA TN 4046.
45. D. R. Chapman. An Approximate Analytical methord for Studying Entry into Planetary Atmospheres. NASA TR R-11, 1959; Supersedes NACA TN 4276.
46. R. E. Slye. An Analytical Methord for Studying the Lateral Motion of Atmosphere Entry Vehicles. NASA TN D-325, 1960.
47. A. Ferri, Ting L.. Practical Aspects of Re-Entry Problems. Astronaut. Acta. 1962(VIII): 63-81
48. H. E. Wang. Approximate Solutions of the Lateral motion of Re-Entry Vehiclesduring Constant Altitude Glide. SSD-TDR-63-60, Aerospace Rept. TDR-169 (3560-10) TN-1, February 25, 1963.
49. H. Youssef, R. Chowdhry, H. Lee, P. Rodi, C. Zimmerman. Predictor-Corrector Entry Guidance for Reusable Launch Vehicles. Proceedings of AIAA Guidance, Navigation, and Control Conference, Montreal, Canada, August, 2001
50. C. Zimmerman, G.. Dukeman, J. Hanson. An Automated Method to Compute Orbital Re-Entry Trajectories with Heating Constraints. Proceedings of AIAA Guidance, Navigation, and Control Conference, Monterey, CA, August, 2002
51. G.. Dukeman. Profile-Following Entry Guidance Using Linear Quadartic Regulator Theory. Proceedings of AIAA Guidance, Navigation, and Control Conference, Monterey, CA, August, 2002
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