Linear and Regular Celestial Mechanics : Perturbed Two-body Motion Numerical Methods Canonical Theory

Eduard L. Stiefel

ISBN 10: 3642650295 / ISBN 13: 9783642650291

Edité par Springer, Springer Gabler, 2011

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - Our presentation of some fundamental domains of celestial mechanics requires no special preliminary knowledge; however, the chosen mathe matical method is new in so far as the pure two-body motion is described by linear differential equations, which even have constant coefficients. In other words an equivalence between the Keplerian motion and a harmonic oscillation is established; this approach to celestial mechanics will be referred to as the linear theory. Besides the possibility of the mutual fruitful interaction between celestial and oscillatory mechanics which is thereby created, our linear differential equations are as a result everywhere regular. The opposite is true of the classical Newtonian equations, which are singular at the collision of the two moving bodies''Reg~larization is however not the leitmotiv of the book; the many regularization methods [1] which do not lead to linear differential equations are therefore not described. Apart from the basic idea of the use of linear differential equations and the resulting advantages, there were two further scientific goals which we had in mind. First, it should be permissible not only to transform the coordinates of the mobile but also to introduce other independent variables instead of the time. The often cumbersome solution of the Keplerian equation in theoretical studies can thereby be avoided. This leads to the further consequence that the linear theory is uniform with respect to the value of the eccentricity.

N° de réf. du vendeur 9783642650291

Détails bibliographiques

• Titre: Linear and Regular Celestial Mechanics : Perturbed Two-body Motion Numerical Methods Canonical Theory
• Éditeur: Springer, Springer Gabler
• Date de parution: 2011
• Langue: anglais
• ISBN à 10 chiffres: 3642650295
• ISBN à 13 chiffres: 9783642650291
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 18 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 18 millimètres de profondeur
• Poids: 493 grammes

A propos de ce titre

Synopsis

Our presentation of some fundamental domains of celestial mechanics requires no special preliminary knowledge; however, the chosen mathe- matical method is new in so far as the pure two-body motion is described by linear differential equations, which even have constant coefficients. In other words an equivalence between the Keplerian motion and a harmonic oscillation is established; this approach to celestial mechanics will be referred to as the linear theory. Besides the possibility of the mutual fruitful interaction between celestial and oscillatory mechanics which is thereby created, our linear differential equations are as a result everywhere regular. The opposite is true of the classical Newtonian equations, which are singular at the collision of the two moving bodies"'Reg larization is however not the leitmotiv of the book; the many regularization methods [1] which do not lead to linear differential equations are therefore not described. Apart from the basic idea of the use of linear differential equations and the resulting advantages, there were two further scientific goals which we had in mind. First, it should be permissible not only to transform the coordinates of the mobile but also to introduce other independent variables instead of the time. The often cumbersome solution of the Keplerian equation in theoretical studies can thereby be avoided. This leads to the further consequence that the linear theory is uniform with respect to the value of the eccentricity.