Geodesic
On integrating the projectile motion equations of a~heavy point in medium with height decreasing density
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 120-132

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The resolvent method based on Legendre transformation was applied to integrate ballistic equations of a heavy point mass in inhomogeneous medium with the drag force being power-law with respect to speed, at that the coefficient of the drag force decreases linearly with height $y$. General expressions were obtained for resolvent function $a''_{bb}(b)$ with $a(b)$ being an intercept and $b=\operatorname{tg}\theta$, where $\theta$ is inclination angle. In the second order by gradient $c/m^{-1}$ of perturbative approach, the universal formulas for $\delta a''_{bb}(b)$-, $\delta x(b)$-, $\delta y(b)$-additions were derived. The case of Releigh resistance was considered particularly in frames of the method above and inhomogeneity influence on the motion was investigated. The falling of gravity $g(y)$ is taken into consideration too.
Mots-clés : Legendre transformation
Keywords: resolvent function, power law air drag, linear density inhomogenity. 
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     author = {V. V. Chistyakov},
     title = {On integrating the projectile motion equations of a~heavy point in medium with height decreasing density},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {120--132},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_1_a9/}
}
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V. V. Chistyakov. On integrating the projectile motion equations of a~heavy point in medium with height decreasing density. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 120-132. http://geodesic.mathdoc.fr/item/VUU_2012_1_a9/