[Chinese translation] Numerical Methods of Celestial Mechanics Foreign entry] [numerical method of celestial mechanics [who] for tink yellow Application of the theory of ordinary differential equations to numerical methods to solve the equations of motion objects. It ﹑ qualitative methods and analysis methods tied to the three basic methods of celestial mechanics. Numerical Methods of Celestial Mechanics, often called a special perturbation method. Coordinate changes in short-period comets fast, can not achieve a major step, it takes a lot of computation time. Encke rectangular objects made by the perturbation variable. This variable changes slowly, steps can be made great, but the calculation much more complicated method to Bike Wei ear. The perturbation method for the variable called Encke method, commonly used in the calculation of short-period comet and the orbit of the moon rocket. Satellite orbital elements of the track is often used as a variable, this is a first-order ordinary differential equations, many-body problem does not have the characteristics of the equations of motion, numerical integration of such issues, you can apply the theory of ordinary differential equations common values Adams method or Runge - Kutta method. Is to determine the stability of numerical methods: a step in the calculation of the error generated in subsequent calculation of the process step by step how to pass along the way, in the transfer process is always bounded and growth, resulting in rapid growth or drowned The results of significant figures. Stability and step on, step greater stability worse. High-precision methods are often too weak and can not be used for stability. The amount of calculation depends on the size of the step and every step of the computation time. With computer calculations, the latter mainly depends on the function of each step calculate the number of differential equations on the right. To _select_ a strong stability of both high precision ﹑ ﹑ small amount of calculation of these three advantages of numerical methods is very difficult. According to these standards for the various traditional methods of evaluation and numerical calculations show that high precision or celestial mechanics a long integration time work should use methods or Adams Kuwait ear method to save computing time, while the Runge - Kutta method can only as an adjunct. For high accuracy, low ﹑ short integration time work, the above methods can use. In recent years, new numerical methods for some special problems of celestial mechanics made some new numerical methods and new research topics, for example, the traditional Taylor series method for ordinary differential equations although it is difficult to use, but for many body problem ﹑ restricted three-body problem has to be successful; there is a numerical method for solution of differential equations of motion of celestial bodies, this is the argument of the trigonometric series and power series or trigonometric series mixing established numerical methods ; there is a known and stable technology, study of this technology is designed to change the equations of motion in the form of days off in order to enhance its stability. Operation of satellites faster than natural bodies, the need for dozens of laps ﹑ numerical integration of hundreds of circles. Stellar group consisting of many-body problem involves hundreds of particles. This gave numerical celestial mechanics put forward new requirements and issues. Bibliography p. henrici, discrete variable methods in ordinary differential equations, john wiley and sons, new york, 1962. elstiefel and g.scheifele, linear and regular celestial mechanics, springer-verlag, berlin, 1971.
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Numerical Methods of Celestial Mechanics: The theory of ordinary differential equations numerical methods to solve the equations of motion objects. It ﹑ qualitative methods and analysis methods tied to the three basic methods of celestial mechanics. Numerical Methods of Celestial Mechanics, often called a special perturbation method. Overview of traditional methods of analysis used in the study of comets and asteroids on the difficulties of movement. These small bodies of the orbital eccentricity and inclination tend to be large, so not according to traditional methods to make them as small parameter series expansion (see perturbation theory). Pluto orbits of large eccentricity of Pluto's movement also caused difficulties. Therefore, the need to use numerical methods to solve. On the days after the satellite, numerical methods and accurate design decisions almost track the primary means of man-made objects. In recent years, this method was also used to study the movement of small stellar systems and many-body problem and other issues. Numerical methods and analysis methods, the advantage of a wide range of applications, the formula is simple, you can achieve very high accuracy; 缺点 is to calculate the step can not get large, need to spend a lot of computation time, only under the conditions of application of computer can be widely used. Obviously, the smaller the step size, the more time spent computing. Celestial mechanics numerical methods dating back to Gauss's method of work. The late nineteenth century methods and the formation of Kuwait ear Adams methods, are still the basic numerical methods of celestial mechanics, but before the advent of the computer, the application is not wide. Coordinate changes in short-period comets fast, can not achieve a major step, it takes a lot of computation time. Encke rectangular objects made by the perturbation variable. This variable changes slowly, steps can be made great, but the calculation much more complicated method to Bike Wei ear. The perturbation method for the variable called Encke method, commonly used in the calculation of short-period comet and the orbit of the moon rocket. Satellite orbital study on the orbital elements are often used as a variable, this is a first-order ordinary differential equations, many-body problem does not have the characteristics of the equations of motion, numerical integration of these issues, you can apply the theory of ordinary differential equations common values Adams method or Runge - Kutta method. Is to determine the stability of numerical methods: a step in the calculation of the error generated in subsequent calculation of the process step by step how to pass along the way, in the transfer process is always bounded and growth, resulting in rapid growth or drowned The results of significant figures. Stability and step on, step greater stability worse. High-precision methods are often too weak and can not be used for stability. The amount of calculation depends on the size of the step and every step of the computation time. With computer calculations, the latter mainly depends on the function of each step calculate the number of differential equations on the right. To _select_ a strong stability of both high precision ﹑ ﹑ small amount of calculation of these three advantages of numerical methods is very difficult. According to these standards for the various traditional methods of evaluation and numerical calculations show that high precision or celestial mechanics a long integration time work should use methods or Adams Kuwait ear method to save computing time, while the Runge - Kutta method can only as an adjunct. For high accuracy, low ﹑ short integration time work, the above methods can use. In recent years, new numerical methods for some special problems of celestial mechanics made some new numerical methods and new research topics, for example, the traditional Taylor series method for ordinary differential equations although it is difficult to use, but for many body problem ﹑ restricted three-body problem has to be successful; there is a numerical method for solution of differential equations of motion of celestial bodies, this is the argument of the trigonometric series and power series or trigonometric series mixing established numerical methods ; there is a known and stable technology, study of this technology is designed to change the equations of motion in the form of days off in order to enhance its stability. Operation of satellites faster than natural bodies, the need for dozens of laps ﹑ numerical integration of hundreds of circles. Stellar group consisting of many-body problem involves hundreds of particles. This gave numerical celestial mechanics put forward new requirements and issues. Bibliography P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, 1962. ELStiefel and G. Scheifele, Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin, 1971.
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tianti lixue shuzhi fangfa Numerical Methods of Celestial Mechanics numerical method of celestial mechanics Application of the theory of ordinary differential equations to numerical methods to solve the equations of motion objects. With analytical methods, qualitative methods tied to the three basic methods of celestial mechanics. Numerical Methods of Celestial Mechanics, often called a special perturbation method. Coordinate changes in short-period comets fast, can not achieve a major step, it takes a lot of computation time. Encke rectangular objects made by the perturbation variable. This variable changes slowly, steps can be made great, but the calculation much more complicated method to Bike Wei ear. The perturbation method for the variable called Encke method, commonly used in the calculation of short-period comet and the orbit of the moon rocket. Satellite orbital study on the orbital elements are often used as a variable, this is a first-order ordinary differential equations, many-body problem does not have the characteristics of the equations of motion. Numerical integration of these issues, you can apply the theory of ordinary differential equations numerical methods or generic Adams Runge - Kutta method. Judge the stability of numerical methods are: calculation error produced a step after step by step in the process of calculation in what way pass along the transmission process are always bounded and growth, or rapid growth which drowned The results of significant figures. Stability and step on, step greater stability worse. High-precision methods are often too weak and can not be used for stability. The amount of calculation depends on the size of the step and every step of the computation time. With computer calculations, the latter mainly depends on the function of each step calculate the number of differential equations on the right. To _select_ a both high precision and stability, a small amount of calculation of these three advantages of numerical methods is very difficult. According to these standards for the various traditional methods of evaluation and numerical calculations show that high precision or celestial mechanics a long integration time work should use methods or Adams Kuwait ear method to save computing time, while the Runge - Kutta method can only as an auxiliary hand