Archive of Issues
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 Academy^{a} 
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 powerlaw 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. 120132. 
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