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Russia Yaroslavl
Section Mechanics
Title On integrating the projectile motion equations of a heavy point in medium with height decreasing density
Author(-s) Chistyakov V.V.a
Affiliations Yaroslavl State Agricultural Academya
Abstract 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 $b={\rm tg}\,\theta$, 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.
Keywords Legendre transformation, resolvent function, power law air drag, linear density inhomogenity
UDC 531.55, 514.85
MSC 70E15, 34A26, 34A34
DOI 10.20537/vm120110
Received 12 December 2011
Language Russian
Citation Chistyakov V.V. On integrating the projectile motion equations of a heavy point in medium with height decreasing density, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 120-132.
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