|
|
Basics of space motion
Bahník, Michal ; Rozehnalová, Petra (referee) ; Kisela, Tomáš (advisor)
This Bachelor thesis is a summarising text which deals with the issue of space motion. We analyse one-body, two-body and three-body problems. We derive analytical solution for the first two problems, from which we derive Kepler's laws, which are important for understanding of the space motion. We also discuss the relation of analytical solution to escape velocities. The closed form of analytical solution for general case of three-body problem does not exist. There are special cases, so-called stable orbits, for which the analytical solution is known. We design the numerical solution by explicit Runge-Kutta-Bogacki-Shampine method and back diferentiation method and we will test the results on the stable orbits.
|
|
|
Application of the Three-Body Problem in the form of exercises
Kolář, Karel ; Šolc, Martin (advisor) ; Franc, Tomáš (referee)
The main topic of this work is the Restricted Three-Body Problem (R3BP) which is illustrated by solving several examples and by simulations in computational system Wolfram Mathematica. The aim is to offer supplemetary material for university students and it can be used also as introduction to this topic for high school students. The first part is dedidated to history of celestial mechanics and to the people who contributed to the development of the R3B Problem. The second chapter consists of simplier tasks with definitions of basic quantities and variables and revision of the undisturbed two-body problem. Subsequent chapters are concentrated to Lagrange points, Jacobi integral, Hill surfaces, tidal force, Tisserand criterion, shape and evolution of close binary stars and other partial tasks.
|
|
|
Application of the Three-Body Problem in the form of exercises
Kolář, Karel ; Šolc, Martin (advisor) ; Franc, Tomáš (referee)
The main topic of this work is the Restricted Three-Body Problem (R3BP) which is illustrated by solving several examples and by simulations in computational system Wolfram Mathematica. The aim is to offer supplemetary material for university students and it can be used also as introduction to this topic for high school students. The first part is dedidated to history of celestial mechanics and to the people who contributed to the development of the R3B Problem. The second chapter consists of simplier tasks with definitions of basic quantities and variables and revision of the undisturbed two-body problem. Subsequent chapters are concentrated to Lagrange points, Jacobi integral, Hill surfaces, tidal force, Tisserand criterion, shape and evolution of close binary stars and other partial tasks.
|
|
|
Basics of space motion
Bahník, Michal ; Rozehnalová, Petra (referee) ; Kisela, Tomáš (advisor)
This Bachelor thesis is a summarising text which deals with the issue of space motion. We analyse one-body, two-body and three-body problems. We derive analytical solution for the first two problems, from which we derive Kepler's laws, which are important for understanding of the space motion. We also discuss the relation of analytical solution to escape velocities. The closed form of analytical solution for general case of three-body problem does not exist. There are special cases, so-called stable orbits, for which the analytical solution is known. We design the numerical solution by explicit Runge-Kutta-Bogacki-Shampine method and back diferentiation method and we will test the results on the stable orbits.
|
guest ::
