Celestial mechanics / by Harry Pollard.

Format:

Book

Author/Creator:

Pollard, Harry, 1919-1985, author.

Series:

Carus mathematical monographs ; Number 18.

Carus Mathematical Monographs ; Number 18

Language:

English

Subjects (All):

Celestial mechanics--Mathematics.

Celestial mechanics.

Physical Description:

1 online resource (x, 134 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington : Mathematical Association of America, 1976.

Language Note:

English

Summary:

The MAA is pleased to re-issue the early Carus Mathematical Monographs in ebook and print-on-demand formats. Readers with an interest in the history of the undergraduate curriculum or the history of a particular field will be rewarded by study of these very clear and approachable little volumes. This monograph presents the basic mathematics underlying the subject of celestial mechanics. Chapter 1 formulates the central force problem and then deals with Kepler's first and second laws, orbits under non-Newtonian attraction, elements of an orbit, the two-body system, the solar system, and disturbed motion. Chapter 2 introduces the n-body problem. Included in Chapter 2 are the Lagrange-Jacobi formula, Sundman's theorem on total collapse, the three-body problem, and Lagrange's and Euler's solutions to the three-body problem. Chapter 3 is an introduction to Hamilton-Jacobi Theory.

Contents:

""11. Determination of the path of a particle""""12. Expansions in elliptic motion""; ""13. Elements of an orbit""; ""14. The two-body problem""; ""15. The solar system""; ""16. Disturbed motion""; ""17. Disturbed motion: variation of the elements""; ""18. Disturbed motion: geometric effects""; ""Chapter Two. Introduction to the N-Body Problem""; ""1. The basic equations: conservation of linear momentum""; ""2. The conservation of energy: the Lagrange-Jacobi formula""; ""3. The conservation of angular momentum""; ""4. Sundman's theorem of total collapse""; ""5. The virial theorem""

""6. Growth of the system""""7. The three-body problem: Jacobi coordinates""; ""8. The Lagrange solutions""; ""9. Euler's solution""; ""10. The restricted three-body problem""; ""11. The circular restricted problem: the Jacobi constant""; ""12. Equilibrium solutions""; ""13. The curves of zero velocity""; ""Chapter Three. Introduction to Hamilton-Jacobi Theory""; ""1. Canonical transformations""; ""2. An application of canonical transformations""; ""3. Canonical transformations generated by a function""; ""4. Generating functions""

""5. Application to the central force and restricted problems""""6. Equilibrium points and their stability""; ""7. Infinitesimal stability""; ""8. The characteristic roots""; ""9. Conditions for stability""; ""10. The stability of the libration points""; ""Index""

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-61444-018-2