Motion in a Central Field in the Presence of a Constant Perturbing Acceleration in a Coordinate System Comoving with the Velocity Vector     

N. Batmunkh  T. N. Sannikova  K. V. Kholshevnikov 《Astronomy Reports》2018,62(4):288-298

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.  相似文献   

Identifying the flow pattern and natural recharge at a strategic groundwater resource in the Dornogobi Province,Mongolia     

Adam Ricka  Tomas Kuchovsky  Batmunkh Damdindorj  Vilem Fürych  Antonin Kopriva  Khukhuu Puntsag 《水文科学杂志》2018,63(9):1408-1423

The strategic project of economic development in the Dornogobi Province in Mongolia is dependent on water supply. Thus a comprehensive hydrogeological characterization was focused on the Upper Cretaceous multi-aquifer system north of Sainshand city. A conceptual model was developed to discover the groundwater flow pattern essential to correct the setting of the numerical model of groundwater flow created using MODFLOW to assess the natural recharge of the aquifer. The conceptualization was based on geological and hydrogeological characterization. However, the evaluation of hydrochemistry proved to be the key factor revealing the principal feature of the groundwater flow pattern, which is the presence of preferential flow zones. These zones allow for intensive transfer of relatively fresh Na(Mg,Ca)?HCO₃-dominated groundwater into discharge areas, where it leaks into the Quaternary aquifer. The numerical model suggested an enormous natural recharge of 22 100 m³/d, originating in 64% of the preferential flow zones.  相似文献   

The norm of the position shift of a celestial body upon variation of its orbit     

N. Batmunkh  T. N. Sannikova  K. V. Kholshevnikov  V. Sh. Shaidulin 《Astronomy Reports》2016,60(3):366-373

A precise estimate of the variation of the position of a celestial body in the case of small variations of the elements of its orbit is obtained using an Euclidean (mean-square) norm for the deviation in the position. A relatively simple expression for the mean-square deviation of the radius vector dr in terms of the deviations of the elements is derived. These are taken to be first-order small quantitites, with second-order quantities neglected. This relation is applied to estimate the norm ||dr|| in two problems. In the first one, small and constant differences between six orbital elements (including the mean anomaly) are considered for two orbits. In the second one, a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration F. The vector F is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the binormal vector. In this latter problem, dr is the difference between the position vectors in the osculating and mean orbit. The norm ||dr||² is the weighted sum of the squares of the components of F, neglecting higher-order small quantities. The coefficients of the quadratic form depend only on the semi-major axis and the eccentricity of the mean orbit. The results are applied to the motion of a small asteroid under the action of a low-thrust engine imparting a small force.  相似文献   

Norm of the Position Shift of a Celestial Body in a Dynamical Astronomy Problem     

K. V. Kholshevnikov  N. Batmunkh  K. I. Oskina  V. B. Titov 《Astronomy Reports》2020,64(4):369-373

The averaging method is widely used in celestial mechanics, in which a mean orbit is introduced and slightly deviates from an osculating one, as long as disturbing forces are small. The difference $$\delta {\mathbf{r}}$$ in the celestial body positions in the mean and osculating orbits is a quasi-periodic function of time. Estimating the norm $$\left\| {\delta {\mathbf{r}}} \right\|$$ for deviation is interesting to note. Earlier, the exact expression of the mean-square norm for one problem of celestial mechanics was obtained: a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration $${\mathbf{F}}$$. The vector $${\mathbf{F}}$$ is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the angular momentum vector. Here, we solved a similar problem, assuming the vector $${\mathbf{F}}$$ to be constant in the reference frame with axes directed along the tangent, the principal normal, and the angular momentum vector. It turned out that $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}$$ is proportional to $${{a}^{6}}$$, where $$a$$ is the semi-major axis. The value $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}{{a}^{{ - 6}}}$$ is the weighted sum of the component squares of $${\mathbf{F}}$$. The quadratic form coefficients depend only on the eccentricity and are represented by the Maclaurin series in even powers of $$e$$ that converge, at least for $$e < 1$$. The series coefficients are calculated up to $${{e}^{4}}$$ inclusive, so that the correction terms are of order $${{e}^{6}}$$.  相似文献