SubjectsSubjects(version: 941)
Course, academic year 2023/2024
   Login via CAS
Celestial Mechanics I - NAST005
Title: Nebeská mechanika I
Guaranteed by: Astronomical Institute of Charles University (32-AUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:4/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. David Vokrouhlický, DrSc.
doc. Mgr. Miroslav Brož, Ph.D.
Classification: Physics > Astronomy and Astrophysics
Is co-requisite for: NAST011
Annotation -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (07.06.2019)
Motion in gravitational field, recapitulation of elements of analytical mechanics. Two-body problem. Three-body problem in two approximations: (i) restricted problem, and (ii) Hill's problem. For students of the first year of master studies in astronomy.
Course completion requirements -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (07.06.2019)

Oral examination preceded by a short written exercise.

Literature -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (04.01.2019)

W.M. Smart, Celestial Mechanics, Longmans, Green and Co., 1953 (nebo ruský překlad)

D. Brouwer, and G. Clemence, Methods of Celestial Mechanics, Academic Press, New York, 1961

C.D. Murray, and S.F. Dermott, Solar System Dynamics, Cambridge University Press, 2008

V. Szebehely, Theory of Orbits, Academic Press, 1961

B. Bertotti, P. Farinella, and D. Vokrouhlicky, Physics of the Solar System, Kluwer Academic Press, 2003

Teaching methods - Czech
Last update: T_AUUK (31.03.2008)


Requirements to the exam - Czech
Last update: prof. RNDr. David Vokrouhlický, DrSc. (06.10.2017)

Zkouška sestává z písemné a ústní části. Písemná část obvykle představuje vyřešení příkladu. Nesplnění písemné části však nevylučuje úspěšné složení zkoušky.

Syllabus -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (07.06.2019)
A brief historical overview.

A brief overview of analytical mechanics:
Lagrange and Hamiltonian approach; Lagrange equations of the second kind; Hamilton equations; canonical transformations; Poisson and Lagrange brackets; symplectic matrix; Hamilton-Jacobi equation; particle in one-diemnsional potential.

Two-body problem:
Basic formulation; transformation of barycenter; relative coordinate; momentum and angular momentum integrals; Binet equation; Kepler equation and variants for parabolic and hyperobolic motions; orbital and non-singular orbital elements; solution of the two-body problem using Hamilton-Jacobi equation; Delaunay variables; elliptic expansions (Bessel functions; Hansen functions).

Circular restricted problem of three bodies:
Equations of motion in the inertial and synodic reference systems; Jacobi integral; Tisserand criterion; Hill's planes of zero velocity; stationary solutions (Lagrange points); stability of stationary solutions.

Elliptic restricted problem of three bodies:
Nechvile's transformation to rotating and pulsating coordinate system; non-integrability; stationary solutions and their stability;

Hill's problem:
Jacobi coordinates; equations of motion in synodic reference system; Hill's surfaces of zero velocity; lunar origin; theory of lunar motion; variational solution.

Charles University | Information system of Charles University |