# Mathematical model of the rocket motion relative to a mobile launcher

 1Degtyareva, ЕА, 1Novykov, OV1Yuzhnoye State Design Office, Dnipro, Ukraine Space Sci. & Technol. 2019, 25 ;(3):03-15 https://doi.org/10.15407/knit2019.03.003 Publication Language: Russian Abstract:  Recently, due to geopolitical and economic reasons, it has become necessary to enhance the types of launches of existing launch vehicles. The rocket launches are most advantageous to carry out in the vicinity of Earth equator. The most effective launches options are provided on launching complexes located on floating sea platforms (LP). But restrained LP dimensions do not allow the deployment of the launching complex equipment at the sufficient distance from each other. Besides, the launcher continuously moves in all degrees of freedom because of sea rolling. Hence, one of the key tasks is to ensure the collision-free launch and minimize the area of the impact of the propulsion system (PS) jet on the elements of the mobile launching complex during rocket flight on the initial segment of a trajectory.          Here, we propose the mathematical model of the controlled disturbed motion of a rocket relative to mobile launcher. In addition, we present models for determining the coordinates of characteristic point located on the rocket relative to launcher elements and coordinates of combustion chambers’ jet traces on the surface of the launch pad during rocket flight on the initial trajectory leg. The proposed mathematical models take into account the ensemble of all most significant disturbing factors and allow modeling the disturbed motions of the rocket, floating launcher and determining relative positions of characteristic points located on them. These models were used when developing and verifying the new control law for the rocket launched in the conditions of sea rolling and in the post-flight analysis of Zenit-3SL rockets launched from the sea launch platform. Keywords: mathematical model, rocket flight on the initial trajectory leg
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