Abstract
The motion of a zero-mass point under the action of gravitation toward a central body and a perturbing acceleration P is considered. The magnitude of P is taken to be small compared to the main acceleration due to the gravitation of the central body, and the components of the vector P are taken to be constant in a reference frame with its origin at the central body and its axes directed along the velocity vector, normal to the velocity vector in the plane of the osculating orbit, and along the binormal. The equations in the mean elements were obtained in an earlier study. The algorithm used to solve these equations is given in this study. This algorithm is analogous to one constructed earlier for the case when P is constant in a reference frame tied to the radius vector. The properties of the solutions are similar. The main difference is that, in the most important cases, the quadratures to which the solution reduces lead to non-elementary functions. However, they can be expressed as series in powers of the eccentricity e that converge for e < 1, and often also for e = 1.
Similar content being viewed by others
References
T. N. Sannikova and K. V. Kholshevnikov, Astron. Rep. 58, 945 (2014).
T. N. Sannikova and K. V. Kholshevnikov, Astron. Rep. 59, 806 (2015).
T. N. Sannikova, Vestn. SPb. Univ., Ser. 1: Mat. Mekh. Astron. 59 (1), 171 (2014).
N. N. Bogolyubov and Yu. A. Mitropolsky, AsymptoticalMethods in the Theory of Non-Linear Oscillations (Gordon Breach, 1961; Fizmatlit,Moscow, 1963).
K. V. Kholshevnikov, Asymptotic Methods of Celestial Mechanics (Leningr. Gos. Univ., Leningrad, 1985) [in Russian].
N. I. Akhiezer, Elements of the Theory of Elliptic Functions (Nauka, Fizmatlit, Moscow, 1970; Am. Math. Soc., Providence, RI, 1990).
I. S. Gradshtein, I. M. Ryzhik, V. V. Maksimov, Tables of Integrals, Series and Products (BKhVPeterburg, St. Petersburg, 2011; Academic, New York, 1980).
A. Gurvits, Theory of Analytic and Elliptic Functions (LENAND, Fizmat. Nasledie, Moscow, 2015) [in Russian].
G. M. Fikhtengol’ts, Course of Differential and Integral Calculus (Fizmatlit, Moscow, 2001), Vol. 2 [in Russian].
M. Tikhomandritskii, Theory of Elliptic Integrals and Elliptic Functions (Kniga po Trebovaniyu, Moscow, 2012) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N. Batmunkh, T.N. Sannikova, K.V. Kholshevnikov, 2018, published in Astronomicheskii Zhurnal, 2018, Vol. 95, No. 4, pp. 307–316.
Rights and permissions
About this article
Cite this article
Batmunkh, N., Sannikova, T.N. & Kholshevnikov, K.V. Motion in a Central Field in the Presence of a Constant Perturbing Acceleration in a Coordinate System Comoving with the Velocity Vector. Astron. Rep. 62, 288–298 (2018). https://doi.org/10.1134/S1063772918040029
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063772918040029