author = "Sukhanov, Alexander Alexandrovich",
                title = "Lectures on astrodynamics",
            publisher = "Instituto Nacional de Pesquisas Espaciais",
                 year = "2010",
              address = "S{\~a}o Jos{\'e} dos Campos",
              edition = "6",
             keywords = "engenharia e tecnologia espaciais, astrodynamics, two-body 
                         problem, Keplerian motion, perturbed theory, impulse maneuvers, 
                         orbital maneuvers, Lambert theory, autonomous navigation, least 
                         square method.",
             abstract = "ABSTRACT: These class notes contain an essence of the author's 
                         lectures giving basic knowledge in different areas of 
                         Astrodynamics. The notes begin with necessary mathematical 
                         information (chapter 1). Then a detailed analysis of the two-body 
                         problem is given (chapters 24). The Kepler's laws, the Newton's 
                         law of gravity, and first integrals of the two-body problem are 
                         given in chapter 2. Then the Keplerian motion is analyzed using 
                         both the classical approach (chapter 3) and a universal approach 
                         (chapter 4). The classical approach means an individual 
                         consideration of the motion for different orbit types. The 
                         universal approach gives an effective method of the motion 
                         calculation unified for all orbit types. The perturbed motion is 
                         considered in chapter 5. This chapter gives a brief introduction 
                         into the theory of the perturbed motion and describes influence of 
                         the main natural perturbations, both gravitational and 
                         non-gravitational ones, on the motion. Chapters 25 are applicable 
                         to the both natural and artificial celestial bodies. The 
                         spacecraft impulsive maneuvers changing different orbital 
                         parameters and performing inter-orbital transfers are analyzed in 
                         chapter 6. A simplified approach to the maneuver optimization and 
                         analysis is considered in the chapter. Interplanetary transfers 
                         including the gravity assist maneuvers are analyzed in chapter 8. 
                         This analysis uses the patched-conic approach, which is described 
                         in the chapter. The Lambert problem solution (i.e. determination 
                         of the transfer orbit between two given positions in a given time) 
                         also is necessary for the interplanetary transfer calculation. 
                         This problem is analyzed in details and solved in the notes 
                         (chapter 7). An advanced approach is used giving a universal 
                         solution to the problem, i.e. solution unified with respect to the 
                         orbit types and number of complete revolutions. Maneuvering of a 
                         spacecraft in the sphere of influence of a planet is considered in 
                         chapter 9. The goal of this maneuvering is transfer of the 
                         spacecraft approaching the planet from the incoming hyperbola to 
                         an operational orbit. An introduction into the space navigation, 
                         i.e. orbit tracking and determination and orbital correction 
                         maneuvers, is given in chapter 10. Autonomous navigation also is 
                         briefly considered there. The optimization of the orbital 
                         maneuvers based on the Pontryagins maximum principle and Lawdens 
                         primer vector is considered in chapter 12. The basic elements of 
                         the optimization theory and its application to the spacecraft 
                         maneuvering are given in the chapter. The electric propulsion (low 
                         thrust) and some aspects of optimization of the electrically 
                         propelled transfers are considered in chapter 13. Chapter 14 gives 
                         an approach to the optimization of both impulsive and low thrust 
                         if the thrust direction is under a constraint. A method of the 
                         optimization of low-thrust transfer between two given positions is 
                         given in chapter 15. This method is based on a linearization of 
                         the transfer near a close Keplerian orbit. A way of providing any 
                         desired accuracy of the optimization is suggested. The 
                         optimization method is also applicable to the case of constrained 
                         thrust direction considered in chapter 14. Chapter 16 considers a 
                         spiral low-thrust transfer between given orbits; this type of 
                         transfer takes place near a planet. Planar transfers with 
                         transversal thrust between two circular orbits or between circular 
                         and parabolic orbits are considered. For this case simple formulas 
                         for the calculation of the transfer parameters are obtained in 
                         this chapter. A general case of the spiral low thrust transfer 
                         between given orbits in an arbitrary gravity field is considered 
                         in chapter 17. A simple and effective method of the transfer 
                         optimization based on the linearization of motion near reference 
                         orbits is described. The method is applicable to different 
                         transfer types and also in the cases of partly given final orbit 
                         or constrained thrust direction. It is shown that the method gives 
                         a locally optimal solution. The state transition matrix, which is 
                         widely used in different areas of the Astrodynamics, is considered 
                         in chapter 11. In particular, calculation of this matrix is 
                         necessary for the spacecraft navigation and correction maneuvers 
                         and for the transfer optimization considered in chapters 10, 12, 
                         13, 15, 17. An effective method of the state transition matrix 
                         calculation and inversion is described in chapter 11. This method 
                         is based on the matrix decomposition simplifying the matrix 
                         calculation and unifying the matrix for different orbit types. 
                         Chapters 6, 7, 9, 11, 14 17 are based on the methods developed by 
                         the author.",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)}",
           copyholder = "SID/SCD",
             language = "en",
                pages = "244",
                  ibi = "8JMKD3MGP7W/38S4F82",
                  url = "",
           targetfile = "publicacao.pdf",
        urlaccessdate = "2020, Oct. 31"