Classical and celestial mechanics
Informacje ogólne
Kod przedmiotu: | 0800-PA-CELMECH |
Kod Erasmus / ISCED: |
(brak danych)
/
(0530) Nauki fizyczne nieokreślone dalej
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Nazwa przedmiotu: | Classical and celestial mechanics |
Jednostka: | Wydział Fizyki, Astronomii i Informatyki Stosowanej |
Grupy: | |
Strona przedmiotu: | https://moodle.umk.pl/course/view.php?id=598 |
Punkty ECTS i inne: |
5.00
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Język prowadzenia: | angielski |
Rodzaj przedmiotu: | przedmiot obowiązkowy |
Całkowity nakład pracy studenta: | (tylko po angielsku) Contact hours with teacher: • participation in lectures - 30 hrs • participation in exercises - 30 hts Self-study hours: • preparation for lectures - 15 hrs • preparation to exercises – 30 hrs • preparation to midterm exams - 30 hrs • preparation to the final exam - 15 hrs Altogether: 150 hrs (5 ECTS) |
Efekty uczenia się - wiedza: | (tylko po angielsku) W1: the basic Newtonian classical mechanics with the focus at the N-body problem and its variants (the planetary problem) W2: the kinematics and dynamics with application of the two-body problem in astrophysics (star-planet, binary stars, planet-moon configurations) W3: the basic theory of the restricted three body problem and its selected application in astrodynamics, galactic dynamics and planetary systems W4: elements of the dynamical systems theory (K_W01, K_W03) |
Efekty uczenia się - umiejętności: | (tylko po angielsku) U1: use of parametrisation of the Keplerian orbits, various types of orbital elements, propagation of the initial condition U2: construction of the kinematic merit function for astrophysical observations of binary systems (radial velocities, astrometry, eclipse timing) U3: numerical integration of the equations of motion (K_U01, K_U02, K_U04) |
Efekty uczenia się - kompetencje społeczne: | (tylko po angielsku) K1: understanding the fundamental links between the mathematical theory and observations K2: understanding the significance of the Copernicus revolution K3: preparation to studying specialized subjects of astronomy (K_K02) |
Metody dydaktyczne: | (tylko po angielsku) Expository teaching methods: • informative (conventional) lecture • classic problem • exercise method |
Skrócony opis: |
(tylko po angielsku) The purpose of the lecture is to discuss basic issues of classical and celestial mechanics centered on the theory of two-body orbits, in the context of the N-body problem and its restricted variants (e.g., the restricted elliptic three-body problem). Modeling observations of binary stars and planetary systems is an important application in the field of astrophysics. Numerical techniques for solving equations of motion and qualitative analysis of simple models, such as the three-body perturbation problem, address basic concepts in dynamical systems theory. The material is intended to be understood by undergraduate students with an elementary background in differential calculus, linear and vector algebra and vector calculus. |
Pełny opis: |
(tylko po angielsku) The topics covered by the course include: 1) The fundamental concepts of Newtonian mechanics, gravitational potential outside uniform sphere (spheroid) and due to uniform disk (ring), generalized coordinates, basics of Lagrangian and Hamiltonian mechanics. 2) The N-body problem in the classical framework, the first integrals of the equations of motion, the virial theorem, the dark matter concept, planetary N-body problem and the equations of motion in relative coordinates, Jacobi variables. 3) The Taylor integration scheme for the ordinary differential equations (ODE) as the canonical method of solving the equations of motion in classical and celestial mechanics, perturbed two body problem (e.g., due to relativistic and non-point mass interactions). 4) The theory of motion in central force fields, qualitative analysis of systems with one-degree of freedom, the two body problem, elements of conic curves theory, Keplerian laws, classification and parametrisation of Keplerian orbits (geometric and dynamical elements). Examples: simple models of motion in galactic gravitational environments (such as the Henon-Heiles model), Sitnikov problem. 5) The two-body orbits kinematic fitting (the Neutsch method) and the merit function for observations made with various techniques (astrometry, eclipse timing, radial velocities), determining the mass function and orbits of binary stars and extrasolar planetary systems. 6) The circular and elliptic restricted three body problems as the fundamental models for astrodynamics (motion of man-made objects in space) and a non-trivial generalisation of the Kepler problem, libration points, elements of the stability and deterministic chaos theory. |
Literatura: |
(tylko po angielsku) The lecture is based on textbooks by Richard Fitzpatrick (Introduction to Celestial Mechanics) and Harry Pollard (Mathematical Introduction to Celestial Mechanics) as well as from other textbooks and to-date scientific papers. The course slides will be published on-line in the form of tme Moodle course. |
Metody i kryteria oceniania: |
(tylko po angielsku) Assessment methods: • midterm exam (4 open problems): W1, W2,W3, W4, U1, U2 • the final written examination (4 open problems): W1, W2, W3, W4, U1, U2, K1, K2 Assessment criteria for each of the midterm exam and the final examinations: fail - below 9 pts (below 50%) satisfactory - 10 pts (51%) satisfactory plus - 12 pts (60%) good - 14 pts (70%) good plus - 16 pts (80%) very good - 18 pts (90%) |
Zajęcia w cyklu "Semestr zimowy 2022/23" (zakończony)
Okres: | 2022-10-01 - 2023-02-19 |
Przejdź do planu
PN WT CW
WYK
ŚR CZ PT |
Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
|
|
Koordynatorzy: | Krzysztof Goździewski | |
Prowadzący grup: | Krzysztof Goździewski, Cezary Migaszewski | |
Lista studentów: | (nie masz dostępu) | |
Zaliczenie: |
Przedmiot -
Egzamin
Ćwiczenia - Zaliczenie na ocenę Wykład - Egzamin |
Zajęcia w cyklu "Semestr zimowy 2023/24" (zakończony)
Okres: | 2023-10-01 - 2024-02-19 |
Przejdź do planu
PN WT ŚR CZ WYK
CW
PT |
Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
|
|
Koordynatorzy: | Krzysztof Goździewski | |
Prowadzący grup: | Krzysztof Goździewski | |
Lista studentów: | (nie masz dostępu) | |
Zaliczenie: |
Przedmiot -
Egzamin
Ćwiczenia - Zaliczenie na ocenę Wykład - Egzamin |
Właścicielem praw autorskich jest Uniwersytet Mikołaja Kopernika w Toruniu.